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)

Question

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 $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

an adult ticket is $8 and a child ticket is $5

Answer 1

Let's denote the cost of an adult ticket as \( A \) and the cost of a child ticket as \( C \). According to the information given:

1. The total cost of three adult and three child tickets is $75: \[ 3A + 3C = 75 \] Simplifying this, we get: \[ A + C = 25 \quad \text{(1)} \]

2. The cost of each child ticket is $3 less than the cost of an adult ticket: \[ C = A - 3 \quad \text{(2)} \]

Now we can substitute equation (2) into equation (1): \[ A + (A - 3) = 25 \] \[ 2A - 3 = 25 \] Adding 3 to both sides, we get: \[ 2A = 28 \] Dividing by 2, we find: \[ A = 14 \]

Now substituting \( A \) back into equation (2) to find \( C \): \[ C = 14 - 3 = 11 \]

Therefore, the price of each adult ticket is $14 and the price of each child ticket is $11.

So the answer is: an adult ticket is $14 and a child ticket is $11.