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Questions: Algebra BusinessCalculus
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$10700 is invested in two different accounts. One account pays 18% simple interest per year and the other account pays 11% simple interest per year. If the total interest earn in one year is $1821.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 18%. Then \(\displaystyle 10700-x\) is amount invested at 11%. This gives the equation \(\displaystyle 0.18 x+0.11(10700 - x)=1821\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 9200\). So the amount in the other account is $1500.
\begin{question}\$10700 is invested in two different accounts. One account pays 18\% simple interest per year and the other account pays 11\% simple interest per year. If the total interest earn in one year is \$1821.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 18\%. Then $10700-x$ is amount invested at 11\%. This gives the equation $0.18 x+0.11(10700 - x)=1821$. Solving for $x$ gives $x = 9200$. So the amount in the other account is \$1500.}
\end{question}
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\end{question}\end{document}<p> <p>$10700 is invested in two different accounts. One account pays 18% simple interest per year and the other account pays 11% simple interest per year. If the total interest earn in one year is $1821.00, 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 18%. Then <img class="equation_image" title=" \displaystyle 10700-x " src="/equation_images/%20%5Cdisplaystyle%2010700-x%20" alt="LaTeX: \displaystyle 10700-x " data-equation-content=" \displaystyle 10700-x " /> is amount invested at 11%. This gives the equation <img class="equation_image" title=" \displaystyle 0.18 x+0.11(10700 - x)=1821 " src="/equation_images/%20%5Cdisplaystyle%200.18%20x%2B0.11%2810700%20-%20x%29%3D1821%20" alt="LaTeX: \displaystyle 0.18 x+0.11(10700 - x)=1821 " data-equation-content=" \displaystyle 0.18 x+0.11(10700 - x)=1821 " /> . 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 = 9200 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%209200%20" alt="LaTeX: \displaystyle x = 9200 " data-equation-content=" \displaystyle x = 9200 " /> . So the amount in the other account is $1500.</p> </p>