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Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an...Question
Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Identify the first step if solving this problem arithmetically, which would find the cost of one adult and one child ticket. (1 point)
Responses
Divide 75 by 6.
Divide 75 by 6.
Divide 75 by 3.
Divide 75 by 3.
Subtract 6 from 75.
Subtract 6 from 75.
Add 3 to 75.
Responses
Divide 75 by 6.
Divide 75 by 6.
Divide 75 by 3.
Divide 75 by 3.
Subtract 6 from 75.
Subtract 6 from 75.
Add 3 to 75.
Answers
Answer
Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Find the price of each ticket.(1 point)
Responses
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $11 and a child ticket is $8
an adult ticket is $11 and a child ticket is $8
an adult ticket is $8 and a child ticket is $5
an adult ticket is $8 and a child ticket is $5
an adult ticket is $14 and a child ticket is $11
an adult ticket is $14 and a child ticket is $11
Responses
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $11 and a child ticket is $8
an adult ticket is $11 and a child ticket is $8
an adult ticket is $8 and a child ticket is $5
an adult ticket is $8 and a child ticket is $5
an adult ticket is $14 and a child ticket is $11
an adult ticket is $14 and a child ticket is $11
Answered by
GPT-4 Turbo
None of the options provided directly finds the cost of one adult and one child ticket using an arithmetic approach that addresses the given relationship between child and adult ticket prices.
The first step should involve setting up equations based on the information provided in the problem.
Let A represent the cost of an adult ticket, and let C represent the cost of a child ticket.
According to the problem, we have two pieces of information:
1. 3 adult tickets and 3 child tickets cost a total of $75:
3A + 3C = 75
2. Each child ticket is $3 less than each adult ticket:
C = A - 3
The goal is to find A and C, so we use the second equation to substitute for C in the first equation.
3A + 3(A - 3) = 75
This would be the correct first step arithmetically in solving the problem. None of the provided options lead to setting up a system of equations, which is necessary for solving this problem. If you have to choose one of the given options as a "first step," you would want to choose one that gets you closer to working with the equations. However, options 1 and 2 do not use the information about the $3 difference. Option 3 merely subtracts 6 from 75 without context. Option 4 adds 3 to 75, which doesn't help in setting up an equation.
The closest (although not completely correct) step from the given options would be to divide 75 by 3, as this could (if followed by correct reasoning) lead to finding the average cost of one ticket (adult or child), which could then be used to set up equations. However, without understanding that each set of 3 tickets includes both adults and children, this step can be misleading.
Correct option based on the provided choices:
Divide 75 by 3.
The first step should involve setting up equations based on the information provided in the problem.
Let A represent the cost of an adult ticket, and let C represent the cost of a child ticket.
According to the problem, we have two pieces of information:
1. 3 adult tickets and 3 child tickets cost a total of $75:
3A + 3C = 75
2. Each child ticket is $3 less than each adult ticket:
C = A - 3
The goal is to find A and C, so we use the second equation to substitute for C in the first equation.
3A + 3(A - 3) = 75
This would be the correct first step arithmetically in solving the problem. None of the provided options lead to setting up a system of equations, which is necessary for solving this problem. If you have to choose one of the given options as a "first step," you would want to choose one that gets you closer to working with the equations. However, options 1 and 2 do not use the information about the $3 difference. Option 3 merely subtracts 6 from 75 without context. Option 4 adds 3 to 75, which doesn't help in setting up an equation.
The closest (although not completely correct) step from the given options would be to divide 75 by 3, as this could (if followed by correct reasoning) lead to finding the average cost of one ticket (adult or child), which could then be used to set up equations. However, without understanding that each set of 3 tickets includes both adults and children, this step can be misleading.
Correct option based on the provided choices:
Divide 75 by 3.
Answered by
GPT-4 Turbo
Let's solve this step by step to find the price of each ticket.
Let A be the cost of an adult ticket.
Let C be the cost of a child ticket.
From the problem statement, we know that:
1. 3 adults plus 3 children tickets cost $75.
2. The child ticket cost is $3 less than the adult ticket cost.
This information leads to two equations:
1. 3A + 3C = 75
2. C = A - 3
Substituting the second equation into the first equation gives:
3A + 3(A - 3) = 75
3A + 3A - 9 = 75
6A - 9 = 75
6A = 75 + 9
6A = 84
A = 84 / 6
A = 14
Now we have the cost of an adult ticket, and we can find the child ticket cost:
C = A - 3
C = 14 - 3
C = 11
Therefore, each adult ticket is $14 and each child ticket is $11.
The correct option is:
an adult ticket is $14 and a child ticket is $11
Let A be the cost of an adult ticket.
Let C be the cost of a child ticket.
From the problem statement, we know that:
1. 3 adults plus 3 children tickets cost $75.
2. The child ticket cost is $3 less than the adult ticket cost.
This information leads to two equations:
1. 3A + 3C = 75
2. C = A - 3
Substituting the second equation into the first equation gives:
3A + 3(A - 3) = 75
3A + 3A - 9 = 75
6A - 9 = 75
6A = 75 + 9
6A = 84
A = 84 / 6
A = 14
Now we have the cost of an adult ticket, and we can find the child ticket cost:
C = A - 3
C = 14 - 3
C = 11
Therefore, each adult ticket is $14 and each child ticket is $11.
The correct option is:
an adult ticket is $14 and a child ticket is $11