ANSWER:
$ 800 was invested in the account at 3%
$5200 was invested in the account at 6%
STEP-BY-STEP EXPLANATION:
We can establish the following system of equations thanks to the help of the statement:
Let x represent the amount invested in the investment that lost value
Let y represent the amount invested in the investment that gained
value.
[tex]\begin{gathered} x+y=6000\rightarrow y=6000-x\text{ (1)} \\ -0.03x+0.06y=288\text{ (2)} \end{gathered}[/tex]We replace equation (1) in (2) and solve for x:
[tex]\begin{gathered} -0.03x+0.06\cdot(6000-x)=288 \\ -0.03x+360-0.06x=288 \\ -0.09x=288-360 \\ x=\frac{-72}{-0.09} \\ x=800 \\ \text{ Now, for y replacing in (1)} \\ y=6000-800=5200 \end{gathered}[/tex]Therefore, $ 800 was invested in the account the lost value, and $ 5200 was invested in the account that gained value.
