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: 3

Answer

The number is 25.

Work Step by Step

step 1 Let x represent the unknown number in the problem. step 2 "$ 20\%$ of itself" = $\displaystyle \frac{20}{100}\cdot x=0.2x$ " ... x is decreased by $ 20\%$ of itself" = $x-0.2x$ " the result is 20" is written as " = 20" step 3 The equation is $x-0.2x=20$ step 4 $ x-0.2x=20\qquad$/simplify LHS $0.8x=20\qquad/\div 0.8$ $x=\displaystyle \frac{20}{0.8}=\frac{200}{8}=25$ The number is $25$. step 5 Check the solution in the original wording of the problem. The number (25), decreased by 20% of 25, ($\displaystyle \frac{20}{100}\cdot 25=5),$ (25-5=20) gives the result 20. OK.
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