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Algebra / Linear functions Difficulty: Hard

Kaylani used fabric measuring $5$ yards in length to make each suit for a men's choir. The relationship between the number of suits that Kaylani made, $x$ , and the total length of fabric that she purchased $y$ , in yards, is represented by the equation $y - 5 x = 6$ . What is the best interpretation of $6$ in this context?

Kaylani made $6$ suits.

Kaylani purchased a total of $6$ yards of fabric.

Kaylani used a total of $6$ yards of fabric to make the suits.

Kaylani purchased $6$ yards more fabric than she used to make the suits.

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Explanation

Choice D is correct. It’s given that the equation $y - 5 x = 6$ represents the relationship between the number of suits that Kaylani made, $x$ , and the total length of fabric she purchased, $y$ , in yards. Adding $5 x$ to both sides of the given equation yields $y = 5 x + 6$ . Since Kaylani made $x$ suits and used $5$ yards of fabric to make each suit, the expression $5 x$ represents the total amount of fabric she used to make the suits. Since $y$ represents the total length of fabric Kaylani purchased, in yards, it follows from the equation $y = 5 x + 6$ that Kaylani purchased $5 x$ yards of fabric to make the suits, plus an additional $6$ yards of fabric. Therefore, the best interpretation of $6$ in this context is that Kaylani purchased $6$ yards more fabric than she used to make the suits.

Choice A is incorrect. Kaylani made a total of $x$ suits, not $6$ suits.

Choice B is incorrect. Kaylani purchased a total of $y$ yards of fabric, not a total of $6$ yards of fabric.

Choice C is incorrect. Kaylani used a total of $5 x$ yards of fabric to make the suits, not a total of $6$ yards of fabric.