Chapter 8.6, Problem 32PPS

To determine

To calculate: the amount invested in each account.

Answer to Problem 32PPS

the amount of the account that earns $9\%$ interest $=6250$

and the amount of the account that earns $5\%$ interest $=3750$

Explanation of Solution

Given information: Judie wants to invest $\$10,000$ in two different accounts. The risky account could earn $9\%$ interest, while the other account earns $5\%$ interest. She wants to earn $\$750$ interest for the year.

Calculation: Judie wants to invest $\$10,000$ in two different accounts. The risky account could earn $9\%$ interest, while the other account earns $5\%$ interest. She wants to earn $\$750$ interest for the year.

Let, the amount of the account that earns $9\%$ interest $=x$

the amount of the account that earns $5\%$ interest $=y$

so $x+y=10,000$

and $0.9x+0.5y=750$

  $\begin{array}{l}x+y=10,000\text{ equation 1}\\ 0.09x+0.05y=750\text{ equation 2 }\end{array}$

  $x=10,000-y$ put in equation $\text{2}$

  $\begin{array}{l}0.09\times \left(10,000-y\right)+0.5y=750\\ 9,00-0.09y+0.05y=750\\ 0.04y=150\\ y=3750\\ x=6250\end{array}$