SAT Math Multiple Choice Practice Question 61: Answer and Explanation

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Question: 61

17. At 1 p.m., a 5-foot-tall boy casts a shadow that is 1 foot, 3 inches long. How tall is a tree that casts a shadow that is 7 feet long at the same time?

A. 35 feet
B. 28 feet
C. 26 feet, 9 inches
D. 10 feet, 9 inches
E. 1 foot, 8 inches

Correct Answer: B


B. This is a classic ratio problem, made more complicated by the presence of both feet and inches. You could convert everything to inches, but because I like fractions (a sad but true statement about my life), I'm going to change 1 foot 3 inches to 11/4 feet. So the ratio says that . Notice that the top numbers stand for the shadows, while the bottom ones stand for the heights of the objects in question. Doing that crazy cross-multiplication thing gives you (11/4)(x) = (5)(7) or 11/4x = 35. Now don't be scared: You have to divide both sides by 11/4, or 5/4. To divide 35 by 5/4, multiply by the reciprocal, or 4/5: 35 × 4/5 = 140/5 = 28.

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