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Questions: Algebra BusinessCalculus
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$8800 is invested in two different accounts. One account pays 19% simple interest per year and the other account pays 24% simple interest per year. If the total interest earn in one year is $2027.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 19%. Then \(\displaystyle 8800-x\) is amount invested at 24%. This gives the equation \(\displaystyle 0.19 x+0.24(8800 - x)=2027\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 1700\). So the amount in the other account is $7100.
\begin{question}\$8800 is invested in two different accounts. One account pays 19\% simple interest per year and the other account pays 24\% simple interest per year. If the total interest earn in one year is \$2027.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 19\%. Then $8800-x$ is amount invested at 24\%. This gives the equation $0.19 x+0.24(8800 - x)=2027$. Solving for $x$ gives $x = 1700$. So the amount in the other account is \$7100.}
\end{question}
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\end{question}\end{document}<p> <p>$8800 is invested in two different accounts. One account pays 19% simple interest per year and the other account pays 24% simple interest per year. If the total interest earn in one year is $2027.00, how much is invested at each rate? </p> </p>
<p> <p>Let <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> be the amount invested at 19%. Then <img class="equation_image" title=" \displaystyle 8800-x " src="/equation_images/%20%5Cdisplaystyle%208800-x%20" alt="LaTeX: \displaystyle 8800-x " data-equation-content=" \displaystyle 8800-x " /> is amount invested at 24%. This gives the equation <img class="equation_image" title=" \displaystyle 0.19 x+0.24(8800 - x)=2027 " src="/equation_images/%20%5Cdisplaystyle%200.19%20x%2B0.24%288800%20-%20x%29%3D2027%20" alt="LaTeX: \displaystyle 0.19 x+0.24(8800 - x)=2027 " data-equation-content=" \displaystyle 0.19 x+0.24(8800 - x)=2027 " /> . Solving for <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x = 1700 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%201700%20" alt="LaTeX: \displaystyle x = 1700 " data-equation-content=" \displaystyle x = 1700 " /> . So the amount in the other account is $7100.</p> </p>