Antoine goes to the mall to buy new shoes and jerseys. He pays a set rate per pair of shoes and a set rate per jersey, and he pays more per jersey than he pays per pair of shoes. His total spending can be modeled by the equation 35x+55y. Which of the statements correctly interprets a part of the expression?

Question

Statement #1: Antoine spends $35.00 per pair of shoes.

Statement #2: Antoine spends $55.00 per pair of shoes.

Statement #3: Antoine spends $35.00 in total for shoes.

Answer 1

The expression \( 35x + 55y \) represents Antoine's total spending, where \( x \) is the number of pairs of shoes he buys and \( y \) is the number of jerseys he buys.

• The coefficient \( 35 \) corresponds to the cost per pair of shoes.
• The coefficient \( 55 \) corresponds to the cost per jersey.

Now let's evaluate each statement:

Statement #1: Antoine spends $35.00 per pair of shoes.
This statement is correct. The coefficient 35 in the expression represents the cost per pair of shoes.

Statement #2: Antoine spends $55.00 per pair of shoes.
This statement is incorrect. The coefficient 55 represents the cost per jersey, not the cost per pair of shoes.

Statement #3: Antoine spends $35.00 in total for shoes.
This statement is incorrect. The total amount spent for shoes would depend on the number of pairs of shoes purchased, represented by \( 35x \). The statement misrepresents the expression as a total amount rather than a per unit cost.

Therefore, the correct interpretation is Statement #1: Antoine spends $35.00 per pair of shoes.