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)

Question

Responses

Subtract 6 from 75.
Subtract 6 from 75.

Divide 75 by 6.
Divide 75 by 6.

Divide 75 by 3.
Divide 75 by 3.

Add 3 to 75......

Answer 1

To solve this problem arithmetically, the first step should be to define the variables for the cost of the adult and child tickets. Let's denote the cost of an adult ticket as \( A \) and the cost of a child ticket as \( C \). According to the problem, we know that:

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

With these equations established, the next logical step would be to substitute the expression for \( C \) into the first equation. This will lead us to combine the two variables and eventually find the values for \( A \) and \( C \).

Given the provided options, we should focus on using the information to structure the equations correctly. Thus, none of the options appear to directly correspond to the first theoretical step in solving the problem mathematically.

However, based on simplifying the situation ahead, the answer that would be part of the logical reasoning (though not the ideal first arithmetic operation), could lead you to start combining the relationships into a form to solve:

Therefore, if I were to choose, none of the options correctly represent the first step as required for the algebraic equation setup. If one must be chosen, focusing on how the costs relate to each other functionally is a better approach than simply subtracting or dividing by a set number.

For completeness, the mathematical structure you should be pursuing should reach a form akin to:

Set an equation based on substituting \( C \) into the total cost equation to solve for either variable, which is ultimately necessary to find the numerical values.

Choosing of options provided, logically understanding to divide the total cost among tickets (albeit incorrect route)???- in practice, that would lead ultimately to an equation balance. In a proper setting with accurate steps chosen and established equations would lead you to work through \( (3A + 3(A - 3) = 75) \) toward solving the actual costs of tickets. In a clear structured way would yield an answer much more direct.

However, none of the given options accurately reflect a purely legitimate starting point.