Carl invests $1,partly in a secure gic at 5% and the rest in a mutual fund that he thinks will earn 7.5%. if he expects to earn the same amount of interest in both, how much did he invest at each rate

Let the amount he invested in the 5% rate be x and the one in the 7.5% rate be y, then
x + y = 10000 . . . (1)
0.05x = 0.075y . . . (2)

From (2), x = 0.075y/0.05 = 1.5y . . . (3)

Putting (3) into (1) gives
1.5y + y = 10000
2.5y = 10000
y = 10000/2.5 = 4000
x = 1.5(4000) = 6000

Therefore, he invested $6,000 in the secure GIC at 5% and $4,000 in the mutual fund.