Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Section 4.4 - Systems of Linear Equations and Problem Solving - Exercise Set: 19

Answer

$27$ nickels $53$ quarters

Work Step by Step

Nickel = 5 cents = 0.05 dollars. Quarters = 25 cents = 0.25 dollars. Let $n$ be the number of nickels. Let $q$ be the number of quarters. A jar containing 80 coins, all of which are either quarters or nickels: $n+q=80$. The total value of the coins is $14.60$: $0.05n+0.25q=14.60$. $n+q=80$ $0.05n+0.25q=14.60$ $q=80-n$ $0.05n+0.25(80-n)=14.60$ $0.05n+20-0.25n=14.60$ $-0.20n+20=14.60$ $-0.20n=-5.40$ $0.20n=5.40$ $n=27$ $n+q=80$ $q=80-n$ $q=80-(27)$ $q=53$ $27$ nickels $53$ quarters
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