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

Divide 75 by 3.
Divide 75 by 3.

Add 3 to 75.
Add 3 to 75.

Subtract 6 from 75.
Subtract 6 from 75.

Divide 75 by 6.

1 answer

To solve this problem arithmetically, the first step is to define the variables representing the costs of the tickets. Let \( A \) be the cost of one adult ticket and \( C \) be the cost of one child ticket. According to the information given, we know the following:

  1. The total cost of three adult tickets and three child tickets is $75.
  2. The cost of a child ticket is $3 less than the cost of an adult ticket: \( C = A - 3 \).

Using these two pieces of information, we can write the equation for the total cost:

\[ 3A + 3C = 75 \]

By substituting \( C \) with \( A - 3 \), we can express everything in terms of \( A \). However, to directly find the cost of one adult and one child ticket, we start by simplifying our equation.

The correct first step in solving this problem would be to divide the entire equation by 3 to make it simpler:

\[ A + C = 25 \]

This allows us to find relationships between the costs of adult and child tickets.

Since the provided options do not accurately represent this step, based on the closest logic structure:

If we are forced to choose one of the provided options, dividing \( 75 \) by \( 6 \) would yield a value that can further lead to the calculations about total costs, even though it does not directly answer the relationship between adult and child tickets.

However, in a more standard approach, direct combination of total prices or solving for \( A \) would have been the preferred method.

But fundamentally, in this context:

The best choice would be: "Divide 75 by 6." (While it's not the ideal first step mathematically, it's the only viable operation from the choices given.)