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Questions: Algebra BusinessCalculus
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$10200 is invested in two different accounts. One account pays 19% simple interest per year and the other account pays 13% simple interest per year. If the total interest earn in one year is $1866.00, how much is invested at each rate?
Let \(\displaystyle x\) be the amount invested at 19%. Then \(\displaystyle 10200-x\) is amount invested at 13%. This gives the equation \(\displaystyle 0.19 x+0.13(10200 - x)=1866\). Solving for \(\displaystyle x\) gives \(\displaystyle x = 9000\). So the amount in the other account is $1200.
\begin{question}\$10200 is invested in two different accounts. One account pays 19\% simple interest per year and the other account pays 13\% simple interest per year. If the total interest earn in one year is \$1866.00, how much is invested at each rate?
\soln{10cm}{Let $x$ be the amount invested at 19\%. Then $10200-x$ is amount invested at 13\%. This gives the equation $0.19 x+0.13(10200 - x)=1866$. Solving for $x$ gives $x = 9000$. So the amount in the other account is \$1200.}
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>$10200 is invested in two different accounts. One account pays 19% simple interest per year and the other account pays 13% simple interest per year. If the total interest earn in one year is $1866.00, 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 19%. Then <img class="equation_image" title=" \displaystyle 10200-x " src="/equation_images/%20%5Cdisplaystyle%2010200-x%20" alt="LaTeX: \displaystyle 10200-x " data-equation-content=" \displaystyle 10200-x " /> is amount invested at 13%. This gives the equation <img class="equation_image" title=" \displaystyle 0.19 x+0.13(10200 - x)=1866 " src="/equation_images/%20%5Cdisplaystyle%200.19%20x%2B0.13%2810200%20-%20x%29%3D1866%20" alt="LaTeX: \displaystyle 0.19 x+0.13(10200 - x)=1866 " data-equation-content=" \displaystyle 0.19 x+0.13(10200 - x)=1866 " /> . 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 = 9000 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%209000%20" alt="LaTeX: \displaystyle x = 9000 " data-equation-content=" \displaystyle x = 9000 " /> . So the amount in the other account is $1200.</p> </p>