Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.3 Applications of Linear Equations - Exercise Set 6.3 - Page 376: 73



Work Step by Step

Assume that the thief has stolen Aplants. After giving one-half of what he has and 2 more plants to first guard, he has \[B\]plants with him. And after giving to the second guard one-half of remaining and 2 more, he has C plants. And after giving to the third guard, he has D plants with him. Express it in algebraic format to obtain, \[\begin{align} & A-\left[ \frac{1}{2}A+2 \right]=B \\ & B-\left[ \frac{1}{2}B+2 \right]=C \\ & C-\left[ \frac{1}{2}C+2 \right]=D \\ \end{align}\] It is provided that at last he has 1 plant with him so, value of Dis 1, now put the value of D in last equation and solving it further we get all values. \[\begin{align} & C-\left[ \frac{1}{2}C+2 \right]=1 \\ & \frac{C}{2}-2=1 \\ & \frac{C}{2}=3 \\ & C=6 \end{align}\] Now substitute back 6 for C in the second equation and solve for B. \[\begin{align} & B-\left[ \frac{1}{2}B+2 \right]=6 \\ & \frac{B}{2}-2=6 \\ & \frac{B}{2}=8 \\ & B=16 \end{align}\] Finally, substitute back 16 for B in the second equation and solve for A. \[\begin{align} & A-\left[ \frac{1}{2}A+2 \right]=16 \\ & \frac{A}{2}-2=16 \\ & \frac{A}{2}=18 \\ & A=36 \end{align}\] So, here the number of plants the thief stole was 36. The thief stole 36 plants.
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