To analyze the expression \(35x + 55\) in the context provided, let's break down the scenario first.
The scenario involves a person who goes to the mall to buy new shoes and jerseys. We know:
- \(x\) represents the number of pairs of shoes purchased.
- The cost of each pair of shoes is $35 (indicated by the coefficient of \(x\)).
- The cost of a jersey is $55 (indicated by the constant term).
The total spending can be modeled by the equation \(35x + 55\).
Now, let's interpret the components of the expression:
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The term \(35x\): This part of the expression represents the total cost of the shoes. Specifically, if someone buys \(x\) pairs of shoes at a rate of $35 per pair, the total cost for shoes will be \(35 \times x\).
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The term \(55\): This represents the fixed cost associated with purchasing one jersey. Thus, irrespective of how many pairs of shoes are bought, there is a one-time cost of $55 for the jersey.
Correct Interpretation of the Expression:
The expression \(35x + 55\) correctly models the total spending where the total cost consists of \(35\) dollars multiplied by the number of pairs of shoes (\(x\)), plus \(55\) dollars for one jersey.
Example Questions:
- If he buys 2 pairs of shoes, what is the total spending?
- If he wants to spend a total of $150, how many pairs of shoes can he buy if he also buys one jersey?
- How much more does he spend on the jersey than on each pair of shoes?
These questions can help test understanding of the expression and its components.
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