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Problem-Solving and Data Analysis / Ratios, rates, proportional relationships, and units Difficulty: Medium

Rectangle A has length 15 and width w. Rectangle B has length 20 and the same length-to-width ratio as rectangle A. What is the width of rectangle B in terms of w ?

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Explanation

Choice A is correct. It’s given that rectangle A has length 15 and width w. Therefore, the length-to-width ratio of rectangle A is 15 to w. It’s also given that rectangle B has length 20 and the same length-to-width ratio as rectangle A. Let x represent the width of rectangle B. The proportion $15 over w, equals, 20 over x$ can be used to solve for x in terms of w. Multiplying both sides of this equation by x yields $the fraction 15 x over w, equals 20$ , and then multiplying both sides of this equation by w yields $15 x equals 20 w$ . Dividing both sides of this equation by 15 yields $x equals, the fraction 20 w over 15$ . Simplifying this fraction yields $x equals, four thirds w$ .

Choices B and D are incorrect and may result from interpreting the difference in the lengths of rectangle A and rectangle B as equivalent to the difference in the widths of rectangle A and rectangle B. Choice C is incorrect and may result from using a length-to-width ratio of w to 15, instead of 15 to w.