Question

Fred received an inheritance of 13,500. He wishes to divide the amount between investments at 15% and 12% to receive an average return on both investments of 13%. How much should he invest at each rate?

If someone can solve the problem but also explain how to setup the problem that would be great. thanks.

Answer 1

We're not going to solve if for you, but we can explain how to set it up:



Suppose $\displaystyle x$ is the amount invested in the account with \ the higher yield and $\displaystyle y\ $is the amount invested in the other then

$\displaystyle \begin{array}{ c c l }
\mathbf{Total\ amount\ of\ Investment} :\ \ & x+y & =13500\\
& \mathbf{and} & \\
\mathbf{Total\ Percentage\ of\ Return} :\ \ & 15\%x+12\%y & =13\%( 13500)
\end{array}$



The two equations above can be solved simulteously as a system.

Answer 2

We're not going to solve if for you, but we can explain how to set it up:



Suppose \(\displaystyle x\) is the amount invested in the account with \ the higher yield and \(\displaystyle y\ \) is the amount invested in the other then

\[\begin{array}{ c c l }
\mathbf{Total\ amount\ of\ Investment} :\ \ & x+y & =13500\\
& \mathbf{and} & \\
\mathbf{Total\ Percentage\ of\ Return} :\ \ & 15\%x+12\%y & =13\%( 13500)
\end{array}\]



The two equations above can be solved simultaneously as a system.