14. James invests a total of $$ \$ 32,000 $$ in two accounts. The first account earned an annual interest rate of $$ 6 \% $$ and the second account earned an annual interest of $$ 3 \% $$ . At the end of one year, the total amount of money gained was $$ \$ 1,380.00 $$ . How much was invested into each account?

Question

14. James invests a total of $$ \$ 32,000 $$ in two accounts. The first account earned an annual interest rate of $$ 6 \% $$ and the second account earned an annual interest of $$ 3 \% $$ . At the end of one year, the total amount of money gained was $$ \$ 1,380.00 $$ . How much was invested into each account?

Gordon John · Accepted Answer

$$\left [ \begin{array} { c } { x + y = 32000 } \ { 0.06 x + 0.03 y = 1380 } \end{array} ight ] $$ Isolate $$ x $$ for $$ x + y = 32000 : x = 32000 - y $$ Substitute $$ x = 32000 - y $$ $$ [ 0.06 ( 32000 - y ) + 0.03 y = 1380 ] $$ Simplify $$ [ 1920 - 0.03 y = 1380 ] $$ Isolate $$ y $$ for $$ 1920 - 0.03 y = 1380 $$ : $$ y = 18000 $$ For $$ x = 32000 - y $$ Substitute $$ y = 18000 $$ $$ x = 32000 - 18000 $$ Simplify $$ x = 14000 $$ The solutions to the system of equations are: $$ x = 14000 , y = 18000$$

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