Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Section 3.2 - Problem Solving and Business Applications Using Systems of Equations - Exercise Set - Page 205: 16

Answer

Investment in the first fund: $\$11,000$. Investment in the second fund: $\$9,000$.

Work Step by Step

Let's note the investment in the first fund by $x$. and the investment in the second fund by $y$. For the last year:- Dividend from the first fund $=8\%$ of $x$. $=0.08x$ Dividend from the second fund $=5\%$ of $y$. $=0.05y$ The total amount received last year is: $\Rightarrow 0.08x+0.05y=1330$...... (1) For this year:- Dividend from the first fund $=12\%$ of $x$. $=0.12x$ Dividend from the second fund $=2\%$ of $y$. $=0.02y$ The total amount received this year is $\Rightarrow 0.12x+0.02y=1500$...... (2) Multiply equation (1) by $-2$. $\Rightarrow -2(0.08x+0.05y)=-2(1330)$ Apply distributive property. $\Rightarrow -0.16x-0.10y=-2660$ ......(3). Multiply equation (2) by $5$. $\Rightarrow 5(0.12x+0.02y)=5(1500)$ Apply distributive property. $\Rightarrow 0.60x+0.10y=7500$...... (4) Add equations (3) and (4). $\Rightarrow -0.16x-0.10y+0.60x+0.10y=-2660+7500$ Add like terms. $\Rightarrow 0.44x=4840$ Divide both sides by $0.44$. $\Rightarrow \frac{0.44x}{0.44}=\frac{4840}{0.44}$ Simplify. $\Rightarrow x=11,000$ Substitute the value of $x$ into equation (1). $\Rightarrow 0.08(11,000)+0.05y=1330$ Simplify. $\Rightarrow 880+0.05y=1330$ Subtract $880$ from both sides. $\Rightarrow 880+0.05y-880=1330-880$ Simplify. $\Rightarrow 0.05y=450$ Divide both sides by $0.05$. $\Rightarrow \frac{0.05y}{0.05}=\frac{450}{0.05}$ Simplify. $\Rightarrow y=9,000$.
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