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Questions: Algebra BusinessCalculus
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$10500 is invested in two different accounts. One account pays 13% simple interest per year and the other account pays 26% simple interest per year. If the total interest earn in one year is $2210.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 13%. Then \(\displaystyle 10500-x\) is amount invested at 26%. This gives the equation \(\displaystyle 0.13 x+0.26(10500 - x)=2210\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 4000\). So the amount in the other account is $6500.
\begin{question}\$10500 is invested in two different accounts. One account pays 13\% simple interest per year and the other account pays 26\% simple interest per year. If the total interest earn in one year is \$2210.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 13\%. Then $10500-x$ is amount invested at 26\%. This gives the equation $0.13 x+0.26(10500 - x)=2210$. Solving for $x$ gives $x = 4000$. So the amount in the other account is \$6500.}
\end{question}
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\end{question}\end{document}<p> <p>$10500 is invested in two different accounts. One account pays 13% simple interest per year and the other account pays 26% simple interest per year. If the total interest earn in one year is $2210.00, 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 13%. Then <img class="equation_image" title=" \displaystyle 10500-x " src="/equation_images/%20%5Cdisplaystyle%2010500-x%20" alt="LaTeX: \displaystyle 10500-x " data-equation-content=" \displaystyle 10500-x " /> is amount invested at 26%. This gives the equation <img class="equation_image" title=" \displaystyle 0.13 x+0.26(10500 - x)=2210 " src="/equation_images/%20%5Cdisplaystyle%200.13%20x%2B0.26%2810500%20-%20x%29%3D2210%20" alt="LaTeX: \displaystyle 0.13 x+0.26(10500 - x)=2210 " data-equation-content=" \displaystyle 0.13 x+0.26(10500 - x)=2210 " /> . 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 = 4000 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%204000%20" alt="LaTeX: \displaystyle x = 4000 " data-equation-content=" \displaystyle x = 4000 " /> . So the amount in the other account is $6500.</p> </p>