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Questions: Algebra BusinessCalculus
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$14000 is invested in two different accounts. One account pays 14% simple interest per year and the other account pays 26% simple interest per year. If the total interest earn in one year is $3100.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 14%. Then \(\displaystyle 14000-x\) is amount invested at 26%. This gives the equation \(\displaystyle 0.14 x+0.26(14000 - x)=3100\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 4500\). So the amount in the other account is $9500.
\begin{question}\$14000 is invested in two different accounts. One account pays 14\% simple interest per year and the other account pays 26\% simple interest per year. If the total interest earn in one year is \$3100.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 14\%. Then $14000-x$ is amount invested at 26\%. This gives the equation $0.14 x+0.26(14000 - x)=3100$. Solving for $x$ gives $x = 4500$. So the amount in the other account is \$9500.}
\end{question}
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\end{question}\end{document}<p> <p>$14000 is invested in two different accounts. One account pays 14% simple interest per year and the other account pays 26% simple interest per year. If the total interest earn in one year is $3100.00, 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 14%. Then <img class="equation_image" title=" \displaystyle 14000-x " src="/equation_images/%20%5Cdisplaystyle%2014000-x%20" alt="LaTeX: \displaystyle 14000-x " data-equation-content=" \displaystyle 14000-x " /> is amount invested at 26%. This gives the equation <img class="equation_image" title=" \displaystyle 0.14 x+0.26(14000 - x)=3100 " src="/equation_images/%20%5Cdisplaystyle%200.14%20x%2B0.26%2814000%20-%20x%29%3D3100%20" alt="LaTeX: \displaystyle 0.14 x+0.26(14000 - x)=3100 " data-equation-content=" \displaystyle 0.14 x+0.26(14000 - x)=3100 " /> . 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 = 4500 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%204500%20" alt="LaTeX: \displaystyle x = 4500 " data-equation-content=" \displaystyle x = 4500 " /> . So the amount in the other account is $9500.</p> </p>