TPAT-1 Tests - เชาวน์ปัญญา

มาแก้โจทย์นี้ทีละขั้น:

สมมติให้จำนวนผู้ใหญ่ = x คน
จำนวนเด็ก = (8,500 - x) คน
รายได้รวม = (250x) + (150(8,500-x))
แทนค่ารายได้ = 1,995,000
250x + 1,275,000 - 150x = 1,995,000
100x = 720,000
x = 7,200 (จำนวนผู้ใหญ่)
จำนวนเด็ก = 8,500 - 7,200 = 1,300
ผลต่างระหว่างผู้ใหญ่และเด็ก = 7,200 - 1,300 = 5,900

{"correct_answer_key":"b"}

I need to solve this problem about volleyball ticket sales.

Given:

Adult tickets: 250 baht each
Child tickets: 150 baht each
Total attendance: 8,500 people
Total revenue: 1,995,000 baht

Let's denote:

x = number of adults
y = number of children

We have two equations:

x + y = 8,500 (total people)
250x + 150y = 1,995,000 (total revenue)

From equation 1: y = 8,500 - x

Substituting into equation 2: 250x + 150(8,500 - x) = 1,995,000 250x + 1,275,000 - 150x = 1,995,000 100x = 720,000 x = 7,200 (number of adults)

Therefore y = 8,500 - 7,200 = 1,300 (number of children)

The difference between adults and children is 7,200 - 1,300 = 5,900 people.

{"correct_answer_key":"b"}

The problem is asking about ticket sales for a volleyball match. Let me translate the problem:

The prices for a volleyball match are: adults 250 baht each, children 150 baht each. There are 8,500 total attendees. The total revenue from ticket sales is 1,995,000 baht. We want to find the difference between the number of adults and children.

Let's set up equations: Let x = number of adults Let y = number of children

We know: x + y = 8,500 (total attendees) 250x + 150y = 1,995,000 (total revenue)

From the first equation, y = 8,500 - x

Substituting into the second equation: 250x + 150(8,500 - x) = 1,995,000 250x + 1,275,000 - 150x = 1,995,000 100x + 1,275,000 = 1,995,000 100x = 720,000 x = 7,200

So there are 7,200 adults.

Now, y = 8,500 - 7,200 = 1,300 children.

The difference between adults and children is: |7,200 - 1,300| = 5,900

Let me double-check this: Total attendees: 7,200 + 1,300 = 8,500 ✓ Total revenue: 250(7,200) + 150(1,300) = 1,800,000 + 195,000 = 1,995,000 ✓

Actually, let me check my work again. I may have made an error.

x + y = 8,500 250x + 150y = 1,995,000

From the first equation: y = 8,500 - x

Substituting: 250x + 150(8,500 - x) = 1,995,000 250x + 1,275,000 - 150x = 1,995,000 100x + 1,275,000 = 1,995,000 100x = 720,000 x = 7,200

So there are 7,200 adults and 8,500 - 7,200 = 1,300 children.

The difference between the number of adults and children is |7,200 - 1,300| = 5,900.

The answer is 5,900, which corresponds to option B.

Actually, let me be absolutely sure with another check.

We have 7,200 adults and 1,300 children. Total: 7,200 + 1,300 = 8,500 ✓ Revenue: 250(7,200) + 150(1,300) = 1,800,000 + 195,000 = 1,995,000 ✓

Therefore, the difference is 7,200 - 1,300 = 5,900.

The answer is B.

This problem involves solving a system of equations based on ticket sales for a volleyball match.

Given information:

Adult tickets: 250 baht each
Child tickets: 150 baht each
Total attendees: 8,500 people
Total revenue: 1,995,000 baht

Let's define variables:

x = number of adults
y = number of children

This gives us two equations: x + y = 8,500 (total people) 250x + 150y = 1,995,000 (total revenue)

From the first equation: y = 8,500 - x Substituting into the second equation: 250x + 150(8,500 - x) = 1,995,000 250x + 1,275,000 - 150x = 1,995,000 100x + 1,275,000 = 1,995,000 100x = 720,000 x = 7,200 adults

Therefore y = 8,500 - 7,200 = 1,300 children

The difference between adults and children is |7,200 - 1,300| = 5,900

{"correct_answer_key":"b"}

To solve this problem, we need to set up a system of equations based on the given information.

Let:

( x ) = number of adults
( y ) = number of children

We have two pieces of information:

The total number of attendees: ( x + y = 8,500 )
The total revenue from tickets: ( 250x + 150y = 1,995,000 )

We can solve these equations step by step.

Step 1: Solve the first equation for ( y ): [ y = 8,500 - x ]

Step 2: Substitute ( y ) into the second equation: [ 250x + 150(8,500 - x) = 1,995,000 ]

Step 3: Simplify and solve for ( x ): [ 250x + 1,275,000 - 150x = 1,995,000 ] [ 100x = 720,000 ] [ x = 7,200 ]

Step 4: Find ( y ): [ y = 8,500 - 7,200 = 1,300 ]

Thus, the number of adults is 7,200 and the number of children is 1,300. The difference between the number of adults and children is: [ 7,200 - 1,300 = 5,900 ]

The correct answer is:

{"correct_answer_key":"b"}

To solve this problem, we'll set up a system of equations based on the given information.

Given:

Price for adults (A): 250 THB
Price for children (C): 150 THB
Total attendees: 8,500 people
Total revenue: 1,995,000 THB

Let:

( x ) = number of adults
( y ) = number of children

Equations:

( x + y = 8500 ) (total attendees)
( 250x + 150y = 1,995,000 ) (total revenue)

Step 1: Solve for one variable

From the first equation: [ y = 8500 - x ]

Step 2: Substitute into the second equation

[ 250x + 150(8500 - x) = 1,995,000 ] [ 250x + 1,275,000 - 150x = 1,995,000 ] [ 100x + 1,275,000 = 1,995,000 ] [ 100x = 720,000 ] [ x = 7,200 ] (number of adults)

Step 3: Find the number of children

[ y = 8500 - 7200 = 1300 ] (number of children)

Step 4: Calculate the difference

[ 7200 - 1300 = 5900 ]

Answer:

The difference between the number of adults and children is 5,900, which corresponds to option B.

{"correct_answer_key":"b"}

Okay, let's see. The problem is about finding the difference between the number of adults and children who attended a volleyball match. The prices are 250 baht per adult and 150 baht per child. Total attendees are 8,500 people, and the total revenue is 1,995,000 baht. We need to find how many more adults than children there were, or vice versa.

First, I'll set up the equations. Let's let A be the number of adults and C be the number of children. We know two things: the total number of people and the total revenue. So:

A + C = 8,500 (total attendees)
250A + 150C = 1,995,000 (total revenue)

I need to solve these two equations to find A and C, then subtract them to find the difference.

Maybe I can solve the first equation for one variable and substitute into the second. Let's solve for C from the first equation: C = 8,500 - A.

Substitute that into the second equation:

250A + 150(8,500 - A) = 1,995,000

Let me expand that:

250A + 150*8,500 - 150A = 1,995,000

Combine like terms:

(250A - 150A) + 1,275,000 = 1,995,000

100A + 1,275,000 = 1,995,000

Subtract 1,275,000 from both sides:

100A = 1,995,000 - 1,275,000 = 720,000

So, A = 720,000 / 100 = 7,200

Then, C = 8,500 - 7,200 = 1,300

Wait, but the options given are a)7200, b)5900, c)5400, d)4200, e)3600. Hmm, the difference between adults and children would be 7,200 - 1,300 = 5,900. So the answer is B)5900. Let me check the calculations again to be sure.

Total adults: 7,200 * 250 = 1,800,000 baht

Total children: 1,300 * 150 = 195,000 baht

Total revenue: 1,800,000 + 195,000 = 1,995,000 baht. That matches. So the difference is 7,200 - 1,300 = 5,900. So option B is correct.

Let ( A ) be the number of adults and ( C ) be the number of children. We have two equations:

( A + C = 8{,}500 ) (total attendees)
( 250A + 150C = 1{,}995{,}000 ) (total revenue).

Solve for ( C ) from the first equation: ( C = 8{,}500 - A ). Substitute into the second equation:
[ 250A + 150(8{,}500 - A) = 1{,}995{,}000 ]
Simplify:
[ 100A + 1{,}275{,}000 = 1{,}995{,}000 \implies A = 7{,}200 ]
Then, ( C = 8{,}500 - 7{,}200 = 1{,}300 ). The difference is ( 7{,}200 - 1{,}300 = 5{,}900 ).

{"correct_answer_key":"b"}

The question, translated from Thai, asks: "The entrance fee for a volleyball match is as follows: 250 baht per adult and 150 baht per child. According to the rules, there are 8,500 spectators and the income from the entrance fee is 1,995,000 baht. How many more adults than children attended this competition?"

Let 'x' be the number of adults and 'y' be the number of children. We can set up a system of equations:

x + y = 8500 (Total number of spectators)
250x + 150y = 1995000 (Total income)

We can solve for x and y. One way is to multiply the first equation by 150:

150x + 150y = 1275000

Subtract this new equation from the second equation:

(250x + 150y) - (150x + 150y) = 1995000 - 1275000
100x = 720000
x = 7200

Now substitute x back into the first equation:

7200 + y = 8500
y = 1300

The difference between the number of adults and children is x - y = 7200 - 1300 = 5900.

{"correct_answer_key": "b"}

Let 'x' be the number of adults and 'y' be the number of children. We have two equations:

x + y = 8500 (Total number of people)
250x + 150y = 1995000 (Total revenue)

We can solve this system of equations. From equation (1), we get y = 8500 - x. Substituting this into equation (2):

250x + 150(8500 - x) = 1995000 250x + 1275000 - 150x = 1995000 100x = 720000 x = 7200

Now, substitute x back into y = 8500 - x: y = 8500 - 7200 y = 1300

The difference between the number of adults and children is |x - y| = |7200 - 1300| = 5900.

{"correct_answer_key":"b"}

Let 'x' be the number of adults and 'y' be the number of children. We have two equations:

x + y = 8500 (Total number of people)
250x + 150y = 1995000 (Total revenue)

We can solve this system of equations. First, simplify the second equation by dividing by 50:

5x + 3y = 39900

Now, solve for x in the first equation: x = 8500 - y

Substitute this value of x into the simplified second equation:

5(8500 - y) + 3y = 39900 42500 - 5y + 3y = 39900 -2y = -2600 y = 1300 (Number of children)

Now, find x: x = 8500 - 1300 = 7200 (Number of adults)

The difference between the number of adults and children is 7200 - 1300 = 5900.

{"correct_answer_key":"b"}

คำถามเป็นภาษาไทย ถามถึงความแตกต่างของจำนวนผู้ใหญ่และเด็กที่เข้าชมการแข่งขันวอลเลย์บอล โดยกำหนดราคาบัตรผู้ใหญ่และเด็ก จำนวนผู้เข้าชมทั้งหมด และรายได้รวม

คำอธิบาย:

จากโจทย์กำหนดให้ราคาบัตรเข้าชมสำหรับผู้ใหญ่ 250 บาท และสำหรับเด็ก 150 บาท มีผู้เข้าชมทั้งหมด 8,500 คน และรายได้รวมจากการขายบัตร 1,995,000 บาท เราต้องการหาความแตกต่างของจำนวนผู้ใหญ่และเด็กที่เข้าชม

ให้ 'x' แทนจำนวนผู้ใหญ่ และ 'y' แทนจำนวนเด็ก

จากข้อมูลโจทย์ เราสามารถสร้างสองสมการได้ดังนี้:

สมการจำนวนผู้เข้าชมทั้งหมด: x + y = 8500
สมการรายได้รวม: 250x + 150y = 1,995,000

จากสมการที่ 1 เราสามารถเขียน y ในรูปของ x ได้: y = 8500 - x

นำค่า y นี้ไปแทนในสมการที่ 2: 250x + 150(8500 - x) = 1,995,000 250x + 1,275,000 - 150x = 1,995,000 100x = 1,995,000 - 1,275,000 100x = 720,000 x = 7200

จากนั้นแทนค่า x กลับไปในสมการ y = 8500 - x: y = 8500 - 7200 y = 1300

ดังนั้น มีผู้ใหญ่เข้าชม 7200 คน และเด็ก 1300 คน

ความแตกต่างของจำนวนผู้ใหญ่และเด็กคือ |x - y| = |7200 - 1300| = 5900

ดังนั้น จำนวนผู้ใหญ่และเด็กที่เข้าชมการแข่งขันครั้งนี้มีจำนวนต่างกัน 5900 คน ซึ่งตรงกับตัวเลือก b.

{"correct_answer_key":"b"}

ให้ A แทนจำนวนผู้ใหญ่ และ C แทนจำนวนเด็ก จากโจทย์จะได้สมการสองข้อคือ A + C = 8500 (จำนวนผู้เข้าชมทั้งหมด) และ 250A + 150C = 1995000 (รายได้ทั้งหมด) เมื่อแก้ระบบสมการนี้ จะได้ A = 7200 และ C = 1300 ดังนั้น จำนวนผู้ใหญ่และเด็กต่างกัน |7200 - 1300| = 5900 คน ซึ่งตรงกับตัวเลือก b

{"correct_answer_key":"b"}

Let $A$ be the number of adults and $C$ be the number of children. We are given that the total number of attendees is 8,500, so $A + C = 8500$. The price for an adult is 250 baht and for a child is 150 baht. The total revenue is 1,995,000 baht. So, $250A + 150C = 1995000$.

We have a system of two linear equations:

$A + C = 8500$
$250A + 150C = 1995000$

From equation 1, we can express $C$ as $C = 8500 - A$. Substitute this into equation 2: $250A + 150(8500 - A) = 1995000$ $250A + 1275000 - 150A = 1995000$ $100A = 1995000 - 1275000$ $100A = 720000$ $A = \frac{720000}{100}$ $A = 7200$

Now find the number of children using $C = 8500 - A$: $C = 8500 - 7200$ $C = 1300$

The number of adults is 7200 and the number of children is 1300. We need to find the difference between the number of adults and children: Difference = $|A - C| = |7200 - 1300| = 5900$.

The difference in the number of adults and children is 5900.

{"correct_answer_key":"b"}

Explanation: Let A be the number of adults and C be the number of children. We are given:

Total spectators: A + C = 8,500
Total revenue: 250A + 150C = 1,995,000

From equation (1), we can express C as C = 8,500 - A. Substitute this into equation (2): 250A + 150(8,500 - A) = 1,995,000 250A + 1,275,000 - 150A = 1,995,000 100A = 1,995,000 - 1,275,000 100A = 720,000 A = 7,200

Now find the number of children: C = 8,500 - A C = 8,500 - 7,200 C = 1,300

The question asks for the difference between the number of adults and children: Difference = |A - C| = |7,200 - 1,300| = 5,900. This corresponds to option B.

{"correct_answer_key":"b"}

Let 'x' be the number of adults and 'y' be the number of children. We can set up a system of two equations:

x + y = 8500 (total number of attendees)
250x + 150y = 1995000 (total revenue)

We can solve for x and y. From equation 1, y = 8500 - x. Substituting into equation 2:

250x + 150(8500 - x) = 1995000 250x + 1275000 - 150x = 1995000 100x = 720000 x = 7200

Then y = 8500 - 7200 = 1300

The difference between the number of adults and children is 7200 - 1300 = 5900.

{"correct_answer_key":"b"}

โจทย์กำหนดให้

ผู้ใหญ่คนละ 250 บาท
เด็กคนละ 150 บาท
จำนวนผู้เข้าชมรวม 8,500 คน
รายได้รวม 1,995,000 บาท

ให้ x = จำนวนผู้ใหญ่, y = จำนวนเด็ก
จะได้สมการ

x + y = 8,500
250x + 150y = 1,995,000

แก้สมการ
จากสมการที่ 1: y = 8,500 - x
แทนค่าในสมการที่ 2:
250x + 150(8,500 - x) = 1,995,000
250x + 1,275,000 - 150x = 1,995,000
100x = 1,995,000 - 1,275,000
100x = 720,000
x = 7,200

y = 8,500 - 7,200 = 1,300

จำนวนต่างกัน = |7,200 - 1,300| = 5,900

ดังนั้น คำตอบคือข้อ b

{"correct_answer_key":"b"}

สมมติให้จำนวนผู้ใหญ่เป็น x คน และจำนวนเด็กเป็น y คน
จากโจทย์มีผู้เข้าชมทั้งหมด 8,500 คน:
x + y = 8,500

รายได้รวมจากบัตรเข้าชม 1,995,000 บาท:
250x + 150y = 1,995,000

แก้สมการ:
จากสมการแรก y = 8,500 - x

แทนค่าในสมการที่สอง:
250x + 150(8,500 - x) = 1,995,000
250x + 1,275,000 - 150x = 1,995,000
100x = 1,995,000 - 1,275,000
100x = 720,000
x = 7,200

ดังนั้น y = 8,500 - 7,200 = 1,300

จำนวนผู้ใหญ่และเด็กต่างกัน = 7,200 - 1,300 = 5,900

คำตอบคือ 5,900 ซึ่งตรงกับตัวเลือก b

{"correct_answer_key":"b"}

จากโจทย์ เรามีข้อมูลดังนี้:

ผู้ใหญ่เข้าชมคนละ 250 บาท
เด็กเข้าชมคนละ 150 บาท
จำนวนผู้เข้าชมรวม 8,500 คน
รายได้รวม 1,995,000 บาท

สมมติให้:

ผู้ใหญ่เข้าชมเป็น x คน
เด็กเข้าชมเป็น y คน

จากข้อมูล:

x + y = 8,500
250x + 150y = 1,995,000

แก้สมการ: จากสมการ (1): y = 8,500 - x

แทนในสมการ (2): 250x + 150(8,500 - x) = 1,995,000 250x + 1,275,000 - 150x = 1,995,000 (250x - 150x) = 1,995,000 - 1,275,000 100x = 720,000 x = 7,200

ดังนั้น: y = 8,500 - 7,200 = 1,300

จำนวนผู้ใหญ่และเด็กต่างกัน: 7,200 - 1,300 = 5,900

คำตอบคือ 5,900 ซึ่งตรงกับตัวเลือก b

{"correct_answer_key":"b"}

ขั้นแรก ให้กำหนดตัวแปรก่อน
สมมติให้มีผู้ใหญ่ x คน และเด็ก y คน
จะได้สมการดังนี้:

(1) ( x + y = 8500 )
(2) ( 250x + 150y = 1995000 )

จากสมการ (1) เราเขียนใหม่ได้เป็น ( y = 8500 - x )
แทนค่า y ลงในสมการ (2):

[ 250x + 150(8500 - x) = 1995000 ]

แก้สมการ:

[ 250x + 1275000 - 150x = 1995000 ]

[ 100x = 1995000 - 1275000 ]

[ 100x = 720000 ]

[ x = 7200 ]

ดังนั้น จำนวนผู้ใหญ่คือ 7200 คน
จำนวนเด็กคือ (8500 - 7200 = 1300) คน

จำนวนที่ต่างกันคือ (7200 - 1300 = 5900) คน ซึ่งตรงกับตัวเลือก b

{"correct_answer_key":"b"}

To solve this problem, we need to set up a system of equations based on the information given:

Let ( x ) be the number of adults and ( y ) be the number of children attending the match.
The total number of people is given by the equation: [ x + y = 8500 ]
The total revenue from ticket sales is given by the equation: [ 250x + 150y = 1995000 ]

We can solve these equations simultaneously to find the values of ( x ) and ( y ).

First, solve the first equation for ( x ): [ x = 8500 - y ]

Substitute ( x = 8500 - y ) into the second equation: [ 250(8500 - y) + 150y = 1995000 ]

Simplify and solve for ( y ): [ 2125000 - 250y + 150y = 1995000 ] [ 2125000 - 100y = 1995000 ] [ 130000 = 100y ] [ y = 1300 ]

Now, substitute ( y = 1300 ) back into the equation for ( x ): [ x = 8500 - 1300 = 7200 ]

The difference in the number of adults and children is: [ x - y = 7200 - 1300 = 5900 ]

Thus, the number of adults and children differs by 5900.

{"correct_answer_key":"b"}

ในการหาจำนวนผู้ใหญ่และเด็กที่เข้าชมการแข่งขันวอลเลย์บอล เราสามารถตั้งสมการได้จากข้อมูลที่ให้มา:

จำนวนผู้เข้าชมทั้งหมด = 8,500 คน
รายได้จากบัตรเข้าชม = 1,995,000 บาท
ราคาบัตรผู้ใหญ่ = 250 บาท
ราคาบัตรเด็ก = 150 บาท

ให้ ( x ) เป็นจำนวนผู้ใหญ่ และ ( y ) เป็นจำนวนเด็ก เราสามารถตั้งสมการได้ดังนี้:

( x + y = 8500 ) (สมการที่ 1)
( 250x + 150y = 1995000 ) (สมการที่ 2)

จากสมการที่ 1 เราสามารถหาค่า ( y ) ได้ว่า ( y = 8500 - x ) แล้วนำไปแทนในสมการที่ 2:

( 250x + 150(8500 - x) = 1995000 )

เมื่อแก้สมการนี้จะได้จำนวนผู้ใหญ่และเด็ก จากนั้นเราสามารถหาค่าต่างกันระหว่างจำนวนผู้ใหญ่และเด็กได้

การคำนวณจะได้ผลลัพธ์ว่า จำนวนผู้ใหญ่และเด็กมีจำนวนต่างกัน 7200 คน ซึ่งตรงกับตัวเลือก A

{"correct_answer_key":"a"}

Let's solve this step by step. We are given that the total number of attendees at a volleyball match is 8,500, with adults paying 250 baht and children paying 150 baht per ticket. The total revenue from ticket sales is 1,995,000 baht. We need to find the difference between the number of adults and children.

Let ( A ) be the number of adults and ( C ) be the number of children. We can set up the following equations based on the given information:

( A + C = 8,500 ) (total number of attendees)
( 250A + 150C = 1,995,000 ) (total revenue)

To solve, we can simplify the second equation by dividing through by 50: ( 5A + 3C = 39,900 )

Now, solve the system of equations. From the first equation, express ( C ) as ( C = 8,500 - A ). Substitute this into the simplified revenue equation: ( 5A + 3(8,500 - A) = 39,900 ) ( 5A + 25,500 - 3A = 39,900 ) ( 2A + 25,500 = 39,900 ) ( 2A = 14,400 ) ( A = 7,200 )

Then, ( C = 8,500 - 7,200 = 1,300 ).

The difference between the number of adults and children is ( |A - C| = |7,200 - 1,300| = 5,900 ).

Thus, the correct answer corresponds to option B.

{"correct_answer_key":"b"}

First, the question is in Thai. Let me translate it to understand it properly.

"ราคาเข้าชมการแข่งขันวอลเลย์บอลนัดหนึ่งเป็นดังนี้ ผู้ใหญ่คนละ 250 บาท และเด็กคนละ 150 บาท ตามข้อกฎว่ามีผู้เข้าชม 8,500 คน และรายได้จากบัตรเข้าชมได้ 1,995,000 บาท อยากทราบว่ามีผู้ใหญ่และเด็กเข้าชมการแข่งขันครั้งนี้มีจำนวนต่างกันกี่คน"

Translated: "The ticket prices for a volleyball match are as follows: Adults 250 baht each and children 150 baht each. It is given that there are 8,500 spectators in total, and the revenue from tickets is 1,995,000 baht. We want to know how many more adults or children attended the match."

The question asks for the difference in the number of adults and children.

Let’s define variables:

Let ( A ) be the number of adults.

Let ( C ) be the number of children.

From the problem:

Total spectators: ( A + C = 8500 )

Total revenue: ( 250A + 150C = 1,995,000 )

We need to find ( |A - C| ), the absolute difference.

First, solve the system of equations.

From the first equation: ( A = 8500 - C )

Substitute into the second:

( 250(8500 - C) + 150C = 1,995,000 )

Calculate 250 * 8500:

250 * 8500 = 250 * 85 * 100 = (250*85)*100

25085: 25080=20,000; 250*5=1,250; total 21,250; then *100=2,125,000? Wait, no:

8500 = 85 * 100, but 250*8500 = 250 * 8500.

Better: 250 * 8500 = 250 * 85 * 100 = first 250*85.

25080=20,000; 2505=1,250; so 20,000+1,250=21,250; then 21,250100? No, 8500 is 8500, not 85100 in that way.

250 * 8500 = 250 * (8000 + 500) = 2508000=2,000,000; 250500=125,000; total 2,000,000 + 125,000 = 2,125,000.

Yes, so 250(8500 - C) = 250*8500 - 250C = 2,125,000 - 250C

Then, equation: 2,125,000 - 250C + 150C = 1,995,000

So, 2,125,000 - 100C = 1,995,000 (since -250C + 150C = -100C)

Now, subtract 2,125,000 from both sides:

-100C = 1,995,000 - 2,125,000

1,995,000 - 2,125,000 = -130,000

So, -100C = -130,000

Divide both sides by -100: C = 130,000 / 100 = 1,300

C = 1,300 children.

Then, A = 8500 - C = 8500 - 1300 = 7,200 adults.

Now, the difference: |A - C| = |7200 - 1300| = 5,900

So, the difference is 5,900 people.

Looking at the options: a:7200, b:5900, c:5400, d:4200, e:3600

So, b:5900 matches.

The question is: "มีผู้ใหญ่และเด็กเข้าชมการแข่งขันครั้งนี้มีจำนวนต่างกันกี่คน" which means "how many people is the difference between adults and children"

Yes, so 5900.

In my calculation, A - C = 7200 - 1300 = 5900, and since it's "different by how many", it's the absolute difference.

So, correct answer is b:5900.

Now, as per the instruction, I need to provide a brief explanation, then respond in JSON with the "correct_answer_key".

Brief explanation: There are 7,200 adults and 1,300 children, so the difference is 7,200 - 1,300 = 5,900.

Then, JSON: {"correct_answer_key":"b"}

Brief Explanation:

The problem involves 8,500 total spectators and ticket revenue of 1,995,000 baht, with adult tickets at 250 baht each and child tickets at 150 baht each. Solving the equations:

Let ( A ) be the number of adults and ( C ) be the number of children.
( A + C = 8500 )
( 250A + 150C = 1,995,000 )

Substitute ( A = 8500 - C ) into the second equation:

( 250(8500 - C) + 150C = 1,995,000 )

( 2,125,000 - 250C + 150C = 1,995,000 )

( 2,125,000 - 100C = 1,995,000 )

( -100C = -130,000 )

( C = 1,300 )

Then, ( A = 8500 - 1,300 = 7,200 )

The difference is ( |A - C| = |7,200 - 1,300| = 5,900 ), which corresponds to option B.

{"correct_answer_key":"b"}

Let's denote the number of adults as A and the number of children as C. We are given two pieces of information:

The total number of spectators is 8,500, so A + C = 8,500.
The total revenue from ticket sales is 1,995,000 baht, with adults paying 250 baht each and children paying 150 baht each, so 250A + 150C = 1,995,000.

We can solve this system of equations to find the values of A and C.

First, let's express C in terms of A from the first equation: C = 8,500 - A.

Now, substitute this expression for C into the second equation: 250A + 150(8,500 - A) = 1,995,000.

Expanding the equation: 250A + 1,275,000 - 150A = 1,995,000.

Combine like terms: 100A = 720,000.

Divide by 100: A = 7,200.

Now, substitute A back into the equation C = 8,500 - A to find C: C = 8,500 - 7,200 = 1,300.

The question asks for the difference in the number of adults and children, which is |A - C| = |7,200 - 1,300| = 5,900.

{"correct_answer_key":"b"}

Let's denote the number of adults as A and the number of children as C. We are given two pieces of information:

A + C = 8500 (total number of attendees)
250A + 150C = 1995000 (total revenue from ticket sales)

We can solve these equations simultaneously to find the values of A and C.

First, let's simplify the second equation by dividing everything by 50: 5A + 3C = 39900

Now, we can multiply the first equation by 3 to help eliminate C when subtracted from the simplified second equation: 3A + 3C = 25500

Subtracting this from the simplified second equation: (5A + 3C) - (3A + 3C) = 39900 - 25500 2A = 14400 A = 7200

Now, substituting A = 7200 into the first equation: 7200 + C = 8500 C = 1300

The difference between the number of adults and children is: |A - C| = |7200 - 1300| = 5900

Thus, the difference in the number of adults and children is 5900, which corresponds to option B.

{"correct_answer_key":"b"}

Let's denote the number of adults as A and the number of children as C.

Given:

A + C = 8500 (total number of people)
250A + 150C = 1995000 (total revenue)

We can solve these equations to find A and C.

From equation 1: C = 8500 - A

Substitute C in equation 2: 250A + 150(8500 - A) = 1995000 250A + 1275000 - 150A = 1995000 100A = 720000 A = 7200

Now, find C: C = 8500 - 7200 = 1300

The difference between the number of adults and children is: |A - C| = |7200 - 1300| = 5900

So, the correct answer is:

{"correct_answer_key":"b"}

To solve this problem, let's denote the number of adults as ( A ) and the number of children as ( C ). We have two pieces of information:

The total number of people is 8,500: [ A + C = 8,500 ]
The total revenue from ticket sales is 1,995,000 baht: [ 250A + 150C = 1,995,000 ]

We can solve these equations simultaneously. First, let's express ( C ) in terms of ( A ) from the first equation: [ C = 8,500 - A ]

Substitute ( C ) into the second equation: [ 250A + 150(8,500 - A) = 1,995,000 ]

Simplify and solve for ( A ): [ 250A + 1,275,000 - 150A = 1,995,000 ] [ 100A + 1,275,000 = 1,995,000 ] [ 100A = 1,995,000 - 1,275,000 ] [ 100A = 720,000 ] [ A = 7,200 ]

Now, find ( C ): [ C = 8,500 - 7,200 ] [ C = 1,300 ]

The difference in the number of adults and children is: [ 7,200 - 1,300 = 5,900 ]

Thus, the correct answer is option B.

{"correct_answer_key":"b"}

คำอธิบายโดยย่อ:
กำหนดให้ x แทนจำนวนผู้ใหญ่ และ y แทนจำนวนเด็ก

x + y = 8,500
250x + 150y = 1,995,000

จากสมการแรก y = 8,500 - x
แทนในสมการที่สอง:
250x + 150(8,500 - x) = 1,995,000
⇒ 250x + 150 × 8,500 - 150x = 1,995,000
⇒ 100x + 1,275,000 = 1,995,000
⇒ 100x = 720,000
⇒ x = 7,200

จำนวนเด็ก (y) = 8,500 - 7,200 = 1,300
ความแตกต่างระหว่างผู้ใหญ่กับเด็ก = 7,200 - 1,300 = 5,900

ดังนั้นคำตอบจึงเป็นข้อ b)

{ "correct_answer_key": "b" }

ผู้ใหญ่ x คน เด็ก y คน

x + y = 8 500 (จำนวนผู้ชมทั้งหมด)
250x + 150y = 1 995 000 (รายได้รวม)

แทน y = 8 500 – x ในสมการ 2
250x + 150(8 500 – x) = 1 995 000
250x + 1 275 000 – 150x = 1 995 000
100x = 720 000 ⇒ x = 7 200 (ผู้ใหญ่)
y = 8 500 – 7 200 = 1 300 (เด็ก)

ส่วนต่างจำนวนผู้ใหญ่และเด็ก = 7 200 – 1 300 = 5 900 คน
ตรงกับตัวเลือกข้อ b.

{"correct_answer_key":"b"}

ราคาบัตรผู้ใหญ่ 250 บาท เด็ก 150 บาท
ให้ x = จำนวนผู้ใหญ่, y = จำนวนเด็ก

x + y = 8 500
250x + 150y = 1 995 000 → หาร 50 ได้ 5x + 3y = 39 900

แทน y = 8 500 − x ลงในสมการที่ 2:
5x + 3(8 500 − x) = 39 900
5x + 25 500 − 3x = 39 900
2x = 14 400 → x = 7 200

ดังนั้น y = 8 500 − 7 200 = 1 300
ต่างกัน = 7 200 − 1 300 = 5 900 คน → ตัวเลือก b

{"correct_answer_key":"b"}

จำนวนผู้ใหญ่ (A) และเด็ก (C) มีสมการ

A + C = 8,500
250A + 150C = 1,995,000

แทน C = 8,500 − A เข้า (2):
250A + 150(8,500 − A) = 1,995,000
250A + 1,275,000 − 150A = 1,995,000
100A = 720,000 ⇒ A = 7,200

ดังนั้น C = 8,500 − 7,200 = 1,300
ผลต่างจำนวนคน = 7,200 − 1,300 = 5,900 ตรงกับตัวเลือก ข้อ b.

{"correct_answer_key":"b"}

Let x be the number of adults and y be the number of children. We have:

x + y = 8500
250x + 150y = 1,995,000

Substitute y = 8500 - x into the second equation: 250x + 150(8500 - x) = 1,995,000
250x + 1,275,000 - 150x = 1,995,000
100x = 720,000
x = 7200

Then, y = 8500 - 7200 = 1300.
The difference between adults and children is 7200 - 1300 = 5900.

{"correct_answer_key":"b"}

Let a = number of adults, c = number of children. We have: a + c = 8500 250a + 150c = 1,995,000 Substitute c = 8500 - a into the revenue equation: 250a + 150(8500 - a) = 1,995,000
250a + 1,275,000 - 150a = 1,995,000
100a = 720,000
a = 7200
Then c = 8500 - 7200 = 1300. The difference is 7200 - 1300 = 5900, which corresponds to option b.

{"correct_answer_key": "b"}

Let x be the number of adults and y be the number of children. We have: x + y = 8500, 250x + 150y = 1995000. Multiplying the first equation by 150 gives: 150x + 150y = 1275000. Subtracting this from the second equation: (250x – 150x) = 1995000 – 1275000 → 100x = 720000, so x = 7200. Then y = 8500 – 7200 = 1300. The difference is 7200 – 1300 = 5900.

{"correct_answer_key": "b"}

เริ่มจากให้ x = จำนวนผู้ใหญ่ และ y = จำนวนเด็ก
จากข้อกำหนด x + y = 8,500 และ 250x + 150y = 1,995,000
แก้สมการได้ x = 7,200 และ y = 1,300
ความต่าง = 7,200 – 1,300 = 5,900

{"correct_answer_key":"b"}

สมการคือ
ผู้ใหญ่ x คน และเด็ก y คน
x + y = 8,500
250x + 150y = 1,995,000

แทน y = 8,500 – x ลงในสมการรายได้
250x + 150(8,500 – x) = 1,995,000
100x + 1,275,000 = 1,995,000
100x = 720,000
x = 7,200 (ผู้ใหญ่), y = 1,300 (เด็ก)
ความต่าง = 7,200 – 1,300 = 5,900

{"correct_answer_key":"b"}

สมการจากข้อมูลคือ
x + y = 8,500 （x = จำนวนผู้ใหญ่, y = จำนวนเด็ก）
250x + 150y = 1,995,000

หารสองสมการแก้ได้ x = 7,200, y = 1,300
ดังนั้นความต่าง = 7,200 – 1,300 = 5,900

{"correct_answer_key":"b"}

ในการแก้ปัญหานี้ เราสามารถใช้สมการเชิงเส้นสองสมการเพื่อหาจำนวนผู้ใหญ่และเด็กที่เข้าชมการแข่งขัน

ให้:

( x ) = จำนวนผู้ใหญ่
( y ) = จำนวนเด็ก

จากข้อมูลที่ให้มา เราสามารถสร้างสมการสองสมการได้ดังนี้:

จำนวนผู้เข้าชมทั้งหมด: [ x + y = 8500 ]
รายได้จากบัตรเข้าชม: [ 250x + 150y = 1995000 ]

เราจะแก้สมการเหล่านี้พร้อมกัน

จากสมการแรก: [ y = 8500 - x ]

แทนค่า ( y ) ในสมการที่สอง: [ 250x + 150(8500 - x) = 1995000 ]

ขยายและทำให้ง่ายขึ้น: [ 250x + 1275000 - 150x = 1995000 ]

[ 100x + 1275000 = 1995000 ]

ลบ 1275000 ออกจากทั้งสองข้าง: [ 100x = 720000 ]

หารด้วย 100: [ x = 7200 ]

แทนค่า ( x ) กลับไปในสมการ ( y = 8500 - x ): [ y = 8500 - 7200 = 1300 ]

ดังนั้น จำนวนผู้ใหญ่และเด็กที่เข้าชมการแข่งขันคือ 7200 คนและ 1300 คน ตามลำดับ ความแตกต่างระหว่างจำนวนผู้ใหญ่และเด็กคือ: [ 7200 - 1300 = 5900 ]

ดังนั้น คำตอบที่ถูกต้องคือ 5900 คน ซึ่งตรงกับตัวเลือก B.

{"correct_answer_key":"b"}

To solve this problem, let's define the variables and set up equations based on the given information:

Variables:

Let $ x $ be the number of adults.
Let $ y $ be the number of children.

Given Information:

Total number of attendees:
$$ x + y = 8,500 $$
Total revenue from ticket sales:
$$ 250x + 150y = 1,995,000 $$

Step 1: Solve the system of equations

From the first equation, solve for $ y $ in terms of $ x $: $$ y = 8,500 - x $$

Substitute $ y = 8,500 - x $ into the second equation: $$ 250x + 150(8,500 - x) = 1,995,000 $$

Simplify: $$ 250x + 150 \cdot 8,500 - 150x = 1,995,000 $$ $$ 250x - 150x + 1,275,000 = 1,995,000 $$ $$ 100x + 1,275,000 = 1,995,000 $$ $$ 100x = 1,995,000 - 1,275,000 $$ $$ 100x = 720,000 $$ $$ x = 7,200 $$

Now substitute $ x = 7,200 $ back into $ y = 8,500 - x $: $$ y = 8,500 - 7,200 = 1,300 $$

Step 2: Find the difference between adults and children

The difference between the number of adults and children is: $$ x - y = 7,200 - 1,300 = 5,900 $$

Final Answer:

The difference between the number of adults and children is 5,900, which corresponds to option b.

{"correct_answer_key":"b"}

Alright, let's tackle this problem step by step. Okay, so the question is about figuring out the difference in the number of adults and children attending a volleyball match. The given information is that the total number of attendees is 8,500, and the total revenue from tickets is 1,995,000 baht. The ticket prices are 250 baht for adults and 150 baht for children.

First, I need to set up some variables. Let me denote the number of adults as 'A' and the number of children as 'C'. The problem gives two pieces of information, so I can create two equations based on that.

The first equation is straightforward: the total number of people. So, A + C = 8500. That's simple enough.

The second equation is about the total revenue. Each adult contributes 250 baht, and each child contributes 150 baht. So, the total revenue would be 250A + 150C = 1,995,000.

Now, I have a system of two equations:

A + C = 8500
250A + 150C = 1,995,000

I need to solve this system to find the values of A and C, and then find the difference between them (A - C or C - A, depending on which is larger).

Let me think about the best way to solve this. Maybe substitution? Since the first equation can be rearranged to express one variable in terms of the other. Let's solve the first equation for A: A = 8500 - C. Then substitute this into the second equation.

Substituting A into the second equation gives:

250*(8500 - C) + 150C = 1,995,000

Let me compute 2508500 first. 250 times 8000 is 2,000,000, and 250500 is 125,000. So total is 2,125,000.

So expanding the equation:

2,125,000 - 250C + 150C = 1,995,000

Combine like terms: -250C + 150C is -100C.

So now:

2,125,000 - 100C = 1,995,000

Subtract 2,125,000 from both sides:

-100C = 1,995,000 - 2,125,000

Calculating the right side: 1,995,000 minus 2,125,000 is -130,000.

So:

-100C = -130,000

Divide both sides by -100:

C = (-130,000)/(-100) = 1,300

Wait, so the number of children is 1,300? Let me check that again because that seems low given the total attendees are 8,500. If C is 1,300, then A would be 8500 - 1300 = 7200.

Let me verify the total revenue with these numbers.

Adults: 7200 * 250 = 1,800,000

Children: 1300 * 150 = 195,000

Adding those together: 1,800,000 + 195,000 = 1,995,000. That matches the given total revenue. Okay, so that checks out.

So the number of adults is 7200 and children is 1300. The question asks for the difference between the number of adults and children.

Calculating the difference: 7200 - 1300 = 5900.

Looking at the options, option b is 5900. So the answer should be B.

Wait, but let me double-check my equations again to make sure I didn't flip anything. The problem says "difference", so it's the absolute difference. Since adults are more, it's 7200 - 1300 = 5900. Yep, that's correct.

Alternatively, maybe I made a mistake in the substitution step. Let me go through the steps again quickly.

Starting with substitution:

A = 8500 - C

Plug into revenue equation:

250*(8500 - C) + 150C = 1,995,000

250*8500 = 2,125,000

So 2,125,000 -250C +150C = 2,125,000 -100C = 1,995,000

Subtract 2,125,000: -100C = -130,000 → C=1300. Correct.

So the difference is indeed 5900. The answer is B.

The problem involves determining the difference between the number of adults and children attending a volleyball match. Let ( A ) be the number of adults and ( C ) the number of children. We set up two equations based on the given information:

Total attendees:
( A + C = 8,!500 )
Total revenue:
( 250A + 150C = 1,!995,!000 )

Solving the first equation for ( A ):
( A = 8,!500 - C )

Substitute into the revenue equation:
( 250(8,!500 - C) + 150C = 1,!995,!000 )
( 2,!125,!000 - 250C + 150C = 1,!995,!000 )
( 2,!125,!000 - 100C = 1,!995,!000 )
( -100C = -130,!000 )
( C = 1,!300 )

Substitute ( C = 1,!300 ) back into ( A = 8,!500 - C ):
( A = 8,!500 - 1,!300 = 7,!200 )

The difference between adults and children is:
( 7,!200 - 1,!300 = 5,!900 ).

{"correct_answer_key":"b"}

Let's denote the number of adults as A and the number of children as C. We know that A + C = 8500 (total number of spectators) and 250A + 150C = 1995000 (total revenue from tickets).

We can express C in terms of A from the first equation: C = 8500 - A.

Substituting this into the second equation gives us: 250A + 150(8500 - A) = 1995000.

Simplifying this equation: 250A + 1275000 - 150A = 1995000.

Combining like terms: 100A = 720000.

Dividing by 100: A = 7200.

Now we can find C: C = 8500 - A = 8500 - 7200 = 1300.

The difference between the number of adults and children is A - C = 7200 - 1300 = 5900.

So, the correct answer is option B.

{"correct_answer_key":"b"}

Alright! Let's tackle this problem step by step. The question is about determining the difference in the number of adults and children who attended a volleyball match based on the given ticket prices and total revenue.

First, I need to parse the information provided. The ticket price for adults is 250 THB each, and for children, it's 150 THB each. The total number of attendees is 8,500 people, and the total revenue from tickets is 1,995,000 THB. The question asks for the difference between the number of adults and children.

To solve this, I can set up a system of equations. Let me denote the number of adults as A and the number of children as C.

The first equation comes from the total number of attendees: A + C = 8,500

The second equation comes from the total revenue: 250A + 150C = 1,995,000

Now, I need to solve these two equations simultaneously. One common method is substitution or elimination. I'll use elimination here.

First, I can simplify the second equation by dividing all terms by 50 to make the numbers smaller and easier to handle: 5A + 3C = 39,900

Now, I have:

A + C = 8,500
5A + 3C = 39,900

I can multiply the first equation by 3 to align the coefficients of C: 3A + 3C = 25,500

Now, subtract this new equation from the simplified second equation: (5A + 3C) - (3A + 3C) = 39,900 - 25,500 This simplifies to: 2A = 14,400 So, A = 7,200

Now that I have the number of adults, I can substitute back into the first equation to find C: 7,200 + C = 8,500 C = 8,500 - 7,200 C = 1,300

The question asks for the difference between the number of adults and children: Difference = A - C = 7,200 - 1,300 = 5,900

Looking at the options provided, option B is 5,900, which matches our calculation.

{
  "correct_answer_key": "b"
}

TPAT-1 Tests - เชาวน์ปัญญา - [12]

Question

Answers by AI

Given:

Let:

Equations:

Step 1: Solve for one variable

Step 2: Substitute into the second equation

Step 3: Find the number of children

Step 4: Calculate the difference

Answer:

Brief Explanation:

Variables:

Given Information:

Step 1: Solve the system of equations

Step 2: Find the difference between adults and children

Final Answer:

TPAT-1 Tests - เชาวน์ปัญญา - [12]

Question

Answers by AI

B claude-3-5-sonnet-20241022 276 new bootstrap.Tooltip(document.getElementById("😭2"));

B claude-3-7-sonnet-20250219 284 new bootstrap.Tooltip(document.getElementById("😭3"));

B claude-3-7-sonnet-20250219[thinking=16k] 1023 new bootstrap.Tooltip(document.getElementById("😭4"));

B command-a-03-2025 411 new bootstrap.Tooltip(document.getElementById("😭5"));

B deepseek-chat-v3-0324 350 new bootstrap.Tooltip(document.getElementById("😭6"));

Given:

Let:

Equations:

Step 1: Solve for one variable

Step 2: Substitute into the second equation

Step 3: Find the number of children

Step 4: Calculate the difference

Answer:

B deepseek-r1 777 new bootstrap.Tooltip(document.getElementById("😭7"));

B gemini-1.5-pro-002 363 new bootstrap.Tooltip(document.getElementById("😭8"));

B gemini-2.0-flash-001 270 new bootstrap.Tooltip(document.getElementById("😭9"));

B gemini-2.0-flash-lite-001 278 new bootstrap.Tooltip(document.getElementById("😭10"));

B gemini-2.0-flash-thinking-exp-01-21 503 new bootstrap.Tooltip(document.getElementById("😭11"));

B gemini-2.5-flash-preview-04-17 1094 new bootstrap.Tooltip(document.getElementById("😭12"));

B gemini-2.5-flash-preview-04-17[no-thinking] 462 new bootstrap.Tooltip(document.getElementById("😭13"));

B gemini-2.5-pro-preview-03-25 1506 new bootstrap.Tooltip(document.getElementById("😭14"));

B gemma-3-27b-it 250 new bootstrap.Tooltip(document.getElementById("😭15"));

B gpt-4.1-2025-04-14 259 new bootstrap.Tooltip(document.getElementById("😭16"));

B gpt-4.1-mini-2025-04-14 245 new bootstrap.Tooltip(document.getElementById("😭17"));

B gpt-4.1-nano-2025-04-14 291 new bootstrap.Tooltip(document.getElementById("😭18"));

B gpt-4.5-preview-2025-02-27 252 new bootstrap.Tooltip(document.getElementById("😭19"));

B gpt-4o-2024-08-06 353 new bootstrap.Tooltip(document.getElementById("😭20"));

A gpt-4o-mini-2024-07-18 299 new bootstrap.Tooltip(document.getElementById("😭21"));

B grok-3-beta 367 new bootstrap.Tooltip(document.getElementById("😭22"));

B grok-3-mini-beta[thinking] 264 new bootstrap.Tooltip(document.getElementById("😭23"));

Brief Explanation:

B llama-3.3-70b-instruct 308 new bootstrap.Tooltip(document.getElementById("😭24"));

B llama-4-maverick 277 new bootstrap.Tooltip(document.getElementById("😭25"));

B llama-4-scout 196 new bootstrap.Tooltip(document.getElementById("😭26"));

B mistral-large-2411 499 new bootstrap.Tooltip(document.getElementById("😭27"));

B o1-2024-12-17 750 new bootstrap.Tooltip(document.getElementById("😭28"));

B o3-2025-04-16[high] 843 new bootstrap.Tooltip(document.getElementById("😭29"));

B o3-2025-04-16[low] 605 new bootstrap.Tooltip(document.getElementById("😭30"));

B o3-2025-04-16[medium] 639 new bootstrap.Tooltip(document.getElementById("😭31"));

B o3-mini-2025-01-31[high] 1067 new bootstrap.Tooltip(document.getElementById("😭32"));

B o3-mini-2025-01-31[low] 683 new bootstrap.Tooltip(document.getElementById("😭33"));

B o3-mini-2025-01-31[medium] 667 new bootstrap.Tooltip(document.getElementById("😭34"));

B o4-mini-2025-04-16[high] 559 new bootstrap.Tooltip(document.getElementById("😭35"));

B o4-mini-2025-04-16[low] 550 new bootstrap.Tooltip(document.getElementById("😭36"));

B o4-mini-2025-04-16[medium] 496 new bootstrap.Tooltip(document.getElementById("😭37"));

B phi-4 683 new bootstrap.Tooltip(document.getElementById("😭38"));

B qwen-max-2025-01-25 529 new bootstrap.Tooltip(document.getElementById("😭39"));

Variables:

Given Information:

Step 1: Solve the system of equations

Step 2: Find the difference between adults and children

Final Answer:

B qwq-32b 1617 new bootstrap.Tooltip(document.getElementById("😭40"));

B typhoon-v2-70b-instruct 224 new bootstrap.Tooltip(document.getElementById("😭41"));

B typhoon-v2-r1-70b-preview 497 new bootstrap.Tooltip(document.getElementById("😭42"));