Precalculus (6th Edition)

Published by Pearson

Chapter 1 - Equations and Inequalities - Quiz - Page 123: 4

Answer

Amount deposited that earns 2.5 percent interest = $\$10,000$Amount deposited that earns 3 percent interest =$\$20,000$

Work Step by Step

Let $x$ = amount invested that earns $2.5\%$ annual interest $2x$ = amount invested that earns $3\%$ annual interest RECALL: The simple interest ($I$) earned is given by the formula: $I=Prt$ where P = principal/amount invested r = annual interest rate t = time The in one year, the investments will earn an interest of: at 2.5 percent: $I=Prt \\I=x(2.5\%)(1) \\I=x(0.025)(1) \\I=0.025x$ at 3 percent: $I=Prt \\I=(2x)(3\%)(1) \\I=(2x)(0.03)(1) \\I=0.06x$ Since te investments earn a total of $\$850$in interest in one year, then$0.025x + 0.06x = \$850 \\(0.025+0.06)x=\$850 \\0.085x = \$850 \\\dfrac{0.085x}(0.085)=\dfrac{\$850}(0.085) \\x=\$10,000$ Thus, $2x=2(\$10,000) = \$20,000$ Therefore the amount deposited are: for the one that earns a 2.5 percent interest = $\$10,000$for the one that earns a 3 percent interest =$\$20,000$

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