Question

Jamie invests part of $10,000 at 9% annual interest and the rest at 8%. If his annual income from

these investments is $860, how much does he invest at 8%?

Answer 1

$4000

Explanation:

Assuming a = money invested at 9%

Assuming b = money invested at 8%

then we can form am equation from the question given

1) a + b = $10000, also

0.09a + 0.08b = $860 -> multiply by 100

2) 9a + 8b = $86000

Next we try to solve both equations simultaneously. We multiply both the left hand side and the right hand side of the first equation by 8. We have

3) 8a + 8b = $80000, now we subtract 3 from 2

9a + 8b = $86000

-8a - 8b = -$80000

a = $6000.

Then, we plug this in any of the first 2 equations, to get b

9 * $6000 + 8b = $86000

$54000 + 8b = $86000

8b = $86000 - $54000

8b = $32000

b = $32000/8

b = $4000.

Therefore, he invested $4000 at 8%