Elementary Algebra

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

Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5: 43

Answer

We invest 2166.66667 dollars, which is approximately 2167 dollars at 5%. We invest 3833.33333 dollars, which is approximately 3833 dollars, at 7%,

Work Step by Step

Let X represent the amount invested at 5%. The remainder, which is 6000 - X, will be invested at 7%. From the first investment we will earn 5% $\times$ X = 0.05X. From the second investment we will earn .07 $\times$ (6000 - X) = 420 - 0.07X. We know that the interest earned by the 5% investment is 160 less than the interest earned by the 7% investment, so we set up the following equation: 0.05X + 160 = 420 - 0.07X 0.12X = 260 Divide both sides by 0.12: X = 2166.66667 dollars, which is approximately 2167 dollars. We invest 2166.66667 dollars, which is approximately 2167 dollars at 5%. We invest 6000 - 2166.66667 = 3833.33333 dollars, which is approximately 3833 dollars, at 7%.
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