Question 1203293
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Here is a very non-standard solution without algebra.  With practice, many similar problems can be solved using the ideas demonstrated in this solution.<br>
The interest of $1130 on a $20,000 investment represents and average rate of return of 1130/20000, which is 5.65%.<br>
Since he invested 3 times as much at 5% as at 4%, 3/4 of the total invested at those two rates was at the higher rate.  That means the average rate of return for those two investments was 3/4 of the way from 4% to 5%; that is 4.75%.<br>
So we can view the investment as one amount at 4.75% and the other amount at 7%.<br>
Now look at the three rates of 4.75%, 5.65%, and 7.00% (on a number line, if it helps), and observe/calculate that 5.65% is 0.90/2.25 = 2/5 of the way from 4.75% to 7%.  That means 2/5 of the total of $20,000 was invested at the higher rate of 7%.  2/5 of $20,000 is $8000, so $8000 was invested at 7%.<br>
That leaves $12,000 invested at 4% or 5%; with 3 times as much invested at 5% as at 4%, simple mental calculations show that $3000 was invested at 4% and $9000 at 5%.<br>
ANSWERS: $3000 at 4%, $9000 at 5%, and $8000 at 7%<br>
CHECK: .04(3000) + .05(9000) + .07(8000) = 120 + 450 + 560 = 1130<br>