Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 54

Mona Galland received a year-end bonus of $\$17,000$ from her company and invested
the money in an account paying $6.5\%$. How much additional money should she deposit in
an account paying $5\%$ so that the return on two investments will be $6\%$?

Step 1: Read the problem, we are asked to find the amount invested in $5\%$ interest rate.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x =$ amount invested in $5\%$ interest rate

$\begin{array}{|c|c|c|c|c|c|} \hline & \rm{Principal} & \cdot & \text{Rate} & = & \rm{Interest} \\ \hline 6.5\% & 17,000 & \cdot & 0.065 & = & 0.065(17,000) \\ \hline 5\% & x & \cdot & 0.05 & = & 0.05(x)\\ \hline \text{Return of Investment} & (x + 17,000) & \cdot & 0.06 & = & 0.06(x + 17,000)\\ \hline \end{array}$


Step 3: Write an equation from the last column of the table
$0.065(17,000) + 0.05x = 0.06(x + 17,000)$

Step 4: Solve

$\begin{equation} \begin{aligned} 1,105 +0.05x &= 0.06x + 1,020\\ \\ 0.05x - 0.06x &= 1,020 - 1,105\\ \\ -0.01x &= -85\\ \\ x &= 8,500 \end{aligned} \end{equation}$


Step 5: State the answer
In other words, the additional invested must be $\$8,500$