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)%0D%0AResponses%0D%0A%0D%0Aan adult ticket is $12.50 and a child ticket is $9.50%0D%0Aan adult ticket is $12.50 and a child ticket is $9.50%0D%0A%0D%0Aan adult ticket is $8 and a child ticket is $5%0D%0Aan adult ticket is $8 and a child ticket is $5%0D%0A%0D%0Aan adult ticket is $14 and a child ticket is $11%0D%0Aan adult ticket is $14 and a child ticket is $11%0D%0A%0D%0Aan adult ticket is $11 and a child ticket is $8
Let's assume the cost of an adult ticket is A and the cost of a child ticket is C.
According to the given information, we know that:
3A + 3C = 75 (Equation 1)
We also know that the cost of each child ticket is $3 less than the cost of an adult ticket:
C = A - 3 (Equation 2)
Now we can solve these equations to find the values of A and C.
Substitute Equation 2 into Equation 1:
3A + 3(A - 3) = 75
3A + 3A - 9 = 75
6A - 9 = 75
Add 9 to both sides:
6A = 84
Divide both sides by 6:
A = 14
Substitute this value back into Equation 2:
C = 14 - 3
C = 11
So the price of each adult ticket is $14 and the price of each child ticket is $11.