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?
Solución de tutoría real
Respuesta rápida
\(\left [ \begin{array} { c } { x + y = 32000 } \\ { 0.06 x + 0.03 y = 1380 } \end{array} \right ] \)
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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