Question

Oscar invests $20,000 in three investments earning 6% ,8% and 10%. He invests $9000 more in the 10% investment than in the 6% investment. How much does he have invested at each rate if he receives $1780 interest the first year?

Answer 1

This problem is mainly concerned with setting up an equation.

let's add the interest rates times their respective investment amounts:


`a = (9000 + x)0.10`


`b = x * 0.06`


`c=(20000 - ((9000 + x) + x)) 0.08`

simplify:


`c = (11000 - 2x) * 0.08`

sum of interest:


`1780 = a + b + c`

1780 = (9000+x) 0.10 + x 0.06 + (11000-2x)0.08


`1780 = 1780 + 0 * x`


`0=0`

solution:

He does not have any invested in the 6%, while he has 9000 invested at 10% and 11,000 invested at 8%

to check:


`9000 * 0.10 + 11000 * 0.08`


`= 900 + 880 = 1780`

So this ended up being a trick problem because he does not actually have any invested in the 6% option.