Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 3 - Equations and Problem Solving - Chapter 3 Review Problem Set: 40

Answer

We have 8 nickels. We have 25 dimes. We have 50 quarters.

Work Step by Step

Let X represent the number of nickels. The number of dimes is 1 more than three times the number of nickels. Three times the number of nickels means 3X 1 more than three times the number of nickels means 3X + 1. So, the number of dimes is 3X + 1. The number of quarters is twice the number of dimes. Since the number of dimes is 3X + 1, the number of quarters is (3X + 1) $\times$ 2 = 6X + 2. One nickel is worth 5 cents, so we have X $\times$ 5 = 5X cents. One dime is worth 10 cents, so we have (3X + 1) $\times$ 10 = 30X + 10 cents. One quarter is worth 25 cents, so we have (6X + 2) $\times$ 25 = 150X + 50 cents. In total, we have 15.40 dollars, which is equal to 1540 cents. Thus, we set up the following equation: 5X + 30X + 10 + 150X + 50 = 1540 185X = 1480 Divide both sides by 185: X = 8 We have 8 nickels. We have 3X + 1 dimes, so we have 3 $\times$ 8 + 1 = 25 dimes. We have 6X + 2 quarters, so we have 6 $\times$ 8 + 2 = 50 quarters.
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