Question 1058544
Let x represent the amount invested in the investment that lost value, 
and let y represent the amount invested in the investment that gained
value.


Since the total investment was $6000, you can write:


x + y = 6000


The total amount gained is then


-0.03x + 0.06y = 288


Solving the first equation for y gives:


y = 6000 - x


Substituting 6000 - x in place of y in the second equation then gives:


-0.03x + 0.06(6000 - x) = 288


-0.03x + 360 - 0.06x = 288


-0.09x + 360 = 288


-0.09x = -72


x = -72 / -0.09


x = 800


Then y = 6000 - 800 = 5200


Solution: $800 was invested in the account the lost value, and $5200 was invested
in the account that gained value.


Check:

x + y = 800 + 5200 = 6000


-0.03x + 0.06y = (-0.03)(800) + (0.06)(5200) = -24 + 312 = 288