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 $14 and a child ticket is $11 an adult ticket is $14 and a child ticket is $11 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 $11 and a child ticket is $8 an adult ticket is $11 and a child ticket is $8 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
Let's assign variables to the adult and child ticket prices. Let A be the cost of an adult ticket and C be the cost of a child ticket.
We know that three adult tickets were purchased, so the cost of the adult tickets is 3A.
We also know that three child tickets were purchased, so the cost of the child tickets is 3C.
The total cost of all the tickets is $75, so we can write the equation: 3A + 3C = 75.
We are also given that the cost of each child ticket is $3 less than the cost of an adult ticket, so we can write another equation: C = A - 3.
Now we have a system of two equations with two variables:
3A + 3C = 75
C = A - 3
We can solve this system of equations to find the values of A and C.
Using substitution method:
Substituting the value of C from the second equation into the first equation:
3A + 3(A - 3) = 75
3A + 3A - 9 = 75
6A - 9 = 75
6A = 75 + 9
6A = 84
A = 84 / 6
A = 14
Now that we have the value of A, we can substitute it back into the second equation to find C:
C = 14 - 3
C = 11
Therefore, the price of each adult ticket is $14 and the price of each child ticket is $11.
The correct answer is: An adult ticket is $14 and a child ticket is $11.