Three adult and tree 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)

Question

A add 3 to 75
B divide 75 by 6
C subtract 6 from 75
D divide 75 by 3

Answer 1

To solve the problem, we want to express the cost of one adult ticket and one child ticket and set up an equation based on the given information.

Let \( A \) be the cost of one adult ticket. Then the cost of one child ticket would be \( A - 3 \).

We know that:

• The total cost for 3 adult tickets and 3 child tickets is $75.

This can be expressed as: \[ 3A + 3(A - 3) = 75 \]

Now, simplifying the left-hand side: \[ 3A + 3A - 9 = 75 \] \[ 6A - 9 = 75 \]

To isolate \( A \), we can first add 9 to both sides, which leads us to: \[ 6A = 75 + 9 \] \[ 6A = 84 \]

Now, dividing both sides by 6 gives: \[ A = 14 \]

Thus, the cost of an adult ticket would be $14 and the cost of a child ticket would be \( 14 - 3 = 11 \).

Looking at the options provided, the first step we would logically take to solve this equation correctly is: A: add 3 to 75 to account for the cost of the child tickets calculated from the adjusted equation.

So the correct answer is: A add 3 to 75.