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?
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.
None of the statements correctly interpret a part of the expression.
The expression 35x + 55y represents Antoine's total spending, where x represents the number of pairs of shoes he buys and y represents the number of jerseys he buys.
Statement #1: This statement incorrectly states that Antoine spends $35.00 per pair of shoes. The expression 35x actually represents the amount Antoine spends on shoes, not the price per pair.
Statement #2: This statement incorrectly states that Antoine spends $55.00 per pair of shoes. The expression 35x + 55y represents Antoine's total spending, including both shoes and jerseys. It does not represent the price per pair of shoes.
Statement #3: This statement incorrectly states that Antoine spends $35.00 in total for shoes. The expression 35x represents the amount Antoine spends on shoes, but the total spending also includes the amount spent on jerseys which is represented by 55y.
The correct statement that interprets a part of the expression is:
Statement #1: Antoine spends $35.00 per pair of shoes.
The expression 35x + 55y represents Antoine's total spending, where x represents the number of pairs of shoes he buys and y represents the number of jerseys he buys.
To determine which statement correctly interprets a part of the expression, let's break it down:
Statement #1: Antoine spends $35.00 per pair of shoes.
This statement is not correct because the expression 35x does not represent the cost per pair of shoes. It represents the total amount Antoine spends on shoes based on the number of pairs he buys.
Statement #2: Antoine spends $55.00 per pair of shoes.
This statement is not correct either because the expression 55y does not represent the cost per pair of shoes. It represents the total amount Antoine spends on jerseys based on the number of jerseys he buys.
Statement #3: Antoine spends $35.00 in total for shoes.
This statement is correct. The coefficient 35 in the expression 35x represents the cost per pair of shoes, and when multiplied by the number of pairs of shoes Antoine buys (represented by x), it gives the total amount he spends on shoes.
Therefore, the correct interpretation is Statement #3: Antoine spends $35.00 in total for shoes.