Declan has n baseball cards. Sam has 4 times as many baseball cards as Declan. Amaya has 7 fewer baseball cards than Sam. Which expression represents the number of baseball cards that Amaya has?
The Correct Answer and Explanation is:
Correct Expression:
The number of baseball cards that Amaya has is represented by the expression:4n−74n – 74n−7
Explanation
To determine how many baseball cards Amaya has, we need to analyze the information given in steps and form expressions based on the relationships described.
- Declan’s Cards:
Declan has n baseball cards. This is the base amount from which we will build our expressions. - Sam’s Cards:
Sam has 4 times as many baseball cards as Declan. This means we multiply Declan’s amount by 4: Sam’s cards=4n\text{Sam’s cards} = 4nSam’s cards=4n - Amaya’s Cards:
Amaya has 7 fewer baseball cards than Sam. The phrase “7 fewer” means we subtract 7 from Sam’s total: Amaya’s cards=4n−7\text{Amaya’s cards} = 4n – 7Amaya’s cards=4n−7
So, the expression 4n – 7 accurately represents how many baseball cards Amaya has in terms of n, the number of cards Declan has.
Why This Expression is Correct:
This problem involves proportional reasoning and subtraction. Let’s break it down conceptually:
- We start with Declan’s amount, n, which is a variable since we don’t know the exact number.
- Sam has four times that amount, so multiplying by 4 is necessary.
- Amaya has less than Sam—not more—so we must subtract, not add.
- Subtracting 7 ensures that Amaya’s total is 7 fewer than Sam’s.
This is a typical example of how algebra can represent real-world relationships using variables and operations. By translating words like “times as many” and “fewer” into multiplication and subtraction, we create a symbolic expression that models the scenario.
Thus, 4n – 7 is the correct algebraic expression for the number of baseball cards Amaya has.
