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Algebra / Linear equations in two variables Difficulty: Medium

Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is $63$ inches. The equation $3 x + 6 y = 63$ represents this situation, where $x$ is the number of sides of figure A and $y$ is the number of sides of figure B. Which statement is the best interpretation of $6$ in this context?

Each side of figure B has a length of $6$ inches.

The number of sides of figure B is $6$ .

Each side of figure A has a length of $6$ inches.

The number of sides of figure A is $6$ .

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Explanation

Choice A is correct. It’s given that figure A and figure B (not shown) are both regular polygons and the sum of the perimeters of the two figures is $63 inches$ . It’s also given that $x$ is the number of sides of figure A and $y$ is the number of sides of figure B, and that the equation $3 x + 6 y = 63$ represents this situation. Thus, $3 x$ and $6 y$ represent the perimeters, in inches, of figure A and figure B, respectively. Since $6 y$ represents the perimeter, in inches, of figure B and $y$ is the number of sides of figure B, it follows that each side of figure B has a length of $6 inches$ .

Choice B is incorrect. The number of sides of figure B is $y$ , not $6$ .

Choice C is incorrect. Since the perimeter, in inches, of figure A is represented by $3 x$ , each side of figure A has a length of $3 inches$ , not $6 inches$ .

Choice D is incorrect. The number of sides of figure A is $x$ , not $6$ .