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Questions: Algebra BusinessCalculus
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$14600 is invested in two different accounts. One account pays 13% simple interest per year and the other account pays 19% simple interest per year. If the total interest earn in one year is $2360.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 13%. Then \(\displaystyle 14600-x\) is amount invested at 19%. This gives the equation \(\displaystyle 0.13 x+0.19(14600 - x)=2360\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 6900\). So the amount in the other account is $7700.
\begin{question}\$14600 is invested in two different accounts. One account pays 13\% simple interest per year and the other account pays 19\% simple interest per year. If the total interest earn in one year is \$2360.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 13\%. Then $14600-x$ is amount invested at 19\%. This gives the equation $0.13 x+0.19(14600 - x)=2360$. Solving for $x$ gives $x = 6900$. So the amount in the other account is \$7700.}
\end{question}
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\end{question}\end{document}<p> <p>$14600 is invested in two different accounts. One account pays 13% simple interest per year and the other account pays 19% simple interest per year. If the total interest earn in one year is $2360.00, 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 14600-x " src="/equation_images/%20%5Cdisplaystyle%2014600-x%20" alt="LaTeX: \displaystyle 14600-x " data-equation-content=" \displaystyle 14600-x " /> is amount invested at 19%. This gives the equation <img class="equation_image" title=" \displaystyle 0.13 x+0.19(14600 - x)=2360 " src="/equation_images/%20%5Cdisplaystyle%200.13%20x%2B0.19%2814600%20-%20x%29%3D2360%20" alt="LaTeX: \displaystyle 0.13 x+0.19(14600 - x)=2360 " data-equation-content=" \displaystyle 0.13 x+0.19(14600 - x)=2360 " /> . 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 = 6900 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%206900%20" alt="LaTeX: \displaystyle x = 6900 " data-equation-content=" \displaystyle x = 6900 " /> . So the amount in the other account is $7700.</p> </p>