Question

Andrew invested $10,000 in two mutual funds. One of the funds rose 6% in one year, and the other rose 9% in one year. If Andrew’s investment rose a total of $684 in one year, how much did he invest in each mutual fund?

Answer 1

Andrew invested $7,200 in the first fund (at 6%) and $2,800 in the second fund (at 9%)

Explanation:

Let $x be Andrew's investment in 1st mutual fund. Then $(10,000-x) is Andrew's investment in 2nd mutual fund.

1st fund:

P = x

r = 0.06 (or 6%)

t = 1 year

Interest
`I_1=P\cdot r\cdot t=x\cdot 0.06\cdot 1=0.06x`

2nd fund:

P = 10,000 - x

r = 0.09 (or 9%)

t = 1 year

Interest
`I_2=P\cdot r\cdot t=(10,000-x)\cdot 0.09\cdot 1=0.09(10,000-x)`

If Andrew’s investment rose a total of $684 in one year, then

`0.06x+0.09(10,000-x)=684\\ \\6x+9(10,000-x)=68,400\\ \\6x+90,000-9x=68,400\\ \\6x-9x=68,400-90,000\\ \\-3x=-21,600\\ \\x=7,200\\ \\10,000-x=10,000-7,200=2,800`