Use the following example to answer the question. 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.

Statement # correctly interprets a part of the expression.

Answer 1

The correct interpretation of the expression \(35x + 55y\) is found in Statement #1.

• Statement #1: Antoine spends $35.00 per pair of shoes. This is correct because the coefficient 35 corresponds to the cost per pair of shoes, and \(x\) represents the number of pairs of shoes he buys.

• Statement #2: Antoine spends $55.00 per pair of shoes. This is incorrect because 55 corresponds to the cost per jersey, not shoes.

• Statement #3: Antoine spends $35.00 in total for shoes. This is also incorrect because the amount Antoine spends on shoes depends on the number of pairs he buys, which is represented by \(x\). The total amount he spends on shoes would be \(35x\), not a fixed $35.00.

Therefore, only Statement #1 correctly interprets a part of the expression.