Intermediate Algebra, Chapter 2, Cumulative Exercises, Section Cumulative Exercises, Problem 32
Shamil Mamedov invested some money at $5\%$ simple interest and $\$2,000$ more than that amount at $6\%$. The interest for the year totaled $\$670$. How much was invested at each rate? Step 1: Read the problem, we are asked to find the amount invested on each rate. Step 2 : Assign the variable. Then organize the information in the table. Let $x = $ amount invested at $5\%$ interest rate. Then, $x + 2000 = $ amount invested at $6\%$ interest rate $ \begin{array}{|c|c|c|c|c|c|} \hline & \rm{Principal} & \cdot & \text{Interest Rate} & = & \rm{Interest} \\ \hline 5 \% & x & \cdot & 0.05 & = & 0.05x \\ \hline 6 \% & x + 2000 & \cdot & 0.06 & = & 0.06(x + 2000) \\ \hline \end{array} $ The total interest earned is equal to the sum of the interests at each rate. Step 3: Write an equation from the last column of the table $0.05x + 0.06(x + 2...