Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Chapter 7 - Measurement - 7.1 Problem Solving with U.S. Measurement Units - 7.1 Exercises - Page 487: 65

Answer

(a) 1.5-2.5 feet tall (b) 8400 months (c) 840 years

Work Step by Step

(a) We convert the minimum and maximum heights of the trees to feet: $18~inches*\frac{1~foot}{12~inches}=1.5~feet=1\frac{1}{2}~feet$ $30~inches*\frac{1~foot}{12~inches}=2.5~feet=2\frac{1}{2}~feet$ Thus the trees are 1.5-2.5 feet tall. (b) We convert years to months: $700~years*\frac{12~months}{1~year}=8400~months$ (c) First, we convert 3 feet to inches in order to use the same units for the comparison: $3~feet*\frac{12~inches}{1~foot}=36~inches$ Next, we set up a proportion to find out how long it would take the tree to reach a height of $36~inches$: $\displaystyle \frac{x}{36~inches}=\frac{700~years}{30~inches}$ We cross-multiply: $30x=700*36$ $30x=25200$ $x=25200/30$ $x=840~years$ Thus it would take 840 years (140 years more).
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