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Questions: Algebra BusinessCalculus
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$8600 is invested in two different accounts. One account pays 24% simple interest per year and the other account pays 9% simple interest per year. If the total interest earn in one year is $849.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 24%. Then \(\displaystyle 8600-x\) is amount invested at 9%. This gives the equation \(\displaystyle 0.24 x+0.09(8600 - x)=849\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 500\). So the amount in the other account is $8100.
\begin{question}\$8600 is invested in two different accounts. One account pays 24\% simple interest per year and the other account pays 9\% simple interest per year. If the total interest earn in one year is \$849.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 24\%. Then $8600-x$ is amount invested at 9\%. This gives the equation $0.24 x+0.09(8600 - x)=849$. Solving for $x$ gives $x = 500$. So the amount in the other account is \$8100.}
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>$8600 is invested in two different accounts. One account pays 24% simple interest per year and the other account pays 9% simple interest per year. If the total interest earn in one year is $849.00, 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 24%. Then <img class="equation_image" title=" \displaystyle 8600-x " src="/equation_images/%20%5Cdisplaystyle%208600-x%20" alt="LaTeX: \displaystyle 8600-x " data-equation-content=" \displaystyle 8600-x " /> is amount invested at 9%. This gives the equation <img class="equation_image" title=" \displaystyle 0.24 x+0.09(8600 - x)=849 " src="/equation_images/%20%5Cdisplaystyle%200.24%20x%2B0.09%288600%20-%20x%29%3D849%20" alt="LaTeX: \displaystyle 0.24 x+0.09(8600 - x)=849 " data-equation-content=" \displaystyle 0.24 x+0.09(8600 - x)=849 " /> . 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 = 500 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20500%20" alt="LaTeX: \displaystyle x = 500 " data-equation-content=" \displaystyle x = 500 " /> . So the amount in the other account is $8100.</p> </p>