Question

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

Add 3 to 75.
Add 3 to 75.

Subtract 6 from 75.
Subtract 6 from 75.

Divide 75 by 3.
Divide 75 by 3.

Divide 75 by 6.

Answer 1

To solve this problem arithmetically, you want to establish a relationship between the cost of adult and child tickets. Let's denote the cost of one adult ticket as \( x \) and the cost of one child ticket as \( x - 3 \) (since the child ticket is $3 less than the adult ticket).

You can set up the equation based on the total amount spent on the tickets:

\[
3x + 3(x - 3) = 75
\]

This simplifies to:

\[
3x + 3x - 9 = 75
\]

Combine like terms:

\[
6x - 9 = 75
\]

To solve for \( x \) (the cost of one adult ticket), the first step would need to isolate \( x \). The correct first step would be to add 9 to both sides:

\[
6x = 75 + 9
\]
\[
6x = 84
\]

Now, to find the adult ticket price, you'd divide by 6.

However, looking at the provided options in your question, the choice that helps in isolating or contributing towards finding the costs is:

**Add 3 to 75.**

This is because it helps you adjust the equation to start solving for the adult ticket cost relative to child tickets. While it's not the direct solution step, it's the closest first arithmetic manipulation that would lead you towards establishing values.