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Questions: Algebra BusinessCalculus
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$12700 is invested in two different accounts. One account pays 10% simple interest per year and the other account pays 27% simple interest per year. If the total interest earn in one year is $2851.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 10%. Then \(\displaystyle 12700-x\) is amount invested at 27%. This gives the equation \(\displaystyle 0.1 x+0.27(12700 - x)=2851\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 3400\). So the amount in the other account is $9300.
\begin{question}\$12700 is invested in two different accounts. One account pays 10\% simple interest per year and the other account pays 27\% simple interest per year. If the total interest earn in one year is \$2851.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 10\%. Then $12700-x$ is amount invested at 27\%. This gives the equation $0.1 x+0.27(12700 - x)=2851$. Solving for $x$ gives $x = 3400$. So the amount in the other account is \$9300.}
\end{question}
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\end{question}\end{document}<p> <p>$12700 is invested in two different accounts. One account pays 10% simple interest per year and the other account pays 27% simple interest per year. If the total interest earn in one year is $2851.00, 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 10%. Then <img class="equation_image" title=" \displaystyle 12700-x " src="/equation_images/%20%5Cdisplaystyle%2012700-x%20" alt="LaTeX: \displaystyle 12700-x " data-equation-content=" \displaystyle 12700-x " /> is amount invested at 27%. This gives the equation <img class="equation_image" title=" \displaystyle 0.1 x+0.27(12700 - x)=2851 " src="/equation_images/%20%5Cdisplaystyle%200.1%20x%2B0.27%2812700%20-%20x%29%3D2851%20" alt="LaTeX: \displaystyle 0.1 x+0.27(12700 - x)=2851 " data-equation-content=" \displaystyle 0.1 x+0.27(12700 - x)=2851 " /> . 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 = 3400 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%203400%20" alt="LaTeX: \displaystyle x = 3400 " data-equation-content=" \displaystyle x = 3400 " /> . So the amount in the other account is $9300.</p> </p>