Question 1175594: An artist invests in a mutual fund account paying 9% and $6000 more than four times as much in a mutual fund account paying 7%. Her total annual interest income from the investments is
$1715. How much does she invest at each rate?
Answer by greenestamps(13196)   (Show Source):
You can put this solution on YOUR website!
I will show a solution method very different from a formal algebraic solution; this method (for me) gets me to the answer much faster than writing and solving an algebraic equation.
Very likely you will get responses from other tutors showing formal algebraic solutions.
First, account for the interest from the "extra" $6000 invested at 7%. That interest is $420. Since the total interest is $1715, the rest of the interest is $1295.
The rest of the investment is some amount at 9% and four times as much at 7%. Various paths using mental arithmetic show that the average interest rate is then 7.4%.
The amount needed to be invested at 7.4% to get $1295 interest is $1295/.074 = $17,500. (No, that part was not mental arithmetic; I used a calculator....)
That $17,500 is split in the ratio 1:4 between the two investments; that means $3500 at 9% and $14,000 at 7%.
ANSWER: $3500 was invested at 9% and $14,000+$6000 = $20,000 was invested at 7%.
CHECK: .09(3500)+.07(20,000) = 315+1400 = 1715
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