SOLUTION: Fred received an inheritance of 13,500. He wishes to divide the amount between investments at 15% and 12% to receive an average return on both investments of 13%. How much should h

Question 1144470: Fred received an inheritance of 13,500. He wishes to divide the amount between investments at 15% and 12% to receive an average return on both investments of 13%. How much should he invest at each rate?
could someone please also explain how to set the problem up
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Fred received an inheritance of 13,500.
He wishes to divide the amount between investments at 15% and 12% to receive an average return on both investments of 13%.
How much should he invest at each rate?
:
let a = amt of 15% investment
let b = amt of 12% investment
:
a + b = 13500
b = (13500 - a); use this form for substitution
and
.15a + .12b = .13(13500)
.15a + .12b = 1755
Replace b with (13500-a)
.15a + .12(13500-a) = 1755
.15a + 1620 - .12a = 1755
.15a - .12a = 1755 - 1620
.03a = 135
a = 135/.03
a = $4500 in the 15% investment
then
13500 - 4500 = $9000 in the 12% investment
:
:
See if that checks out
.15(4500) = 675
.12(9000) = 1080
-------------------
total ret: 1755 which is 13% of 13500

Answer by greenestamps(13258) (Show Source): You can put this solution on YOUR website!

Here is a very simple way to solve this kind of problem without algebra, by looking at how far the average return percentage is between the return percentages from the individual investments.

(1) 13% is 1/3 of the way from 12% to 15%. (If it helps, picture the three percentages 12, 13, and 15, on a number line....)
(2) Therefore, 1/3 of the money should be invested at the higher rate.

ANSWER: 1/3 of the $13,500, or $4500, at 15%; the other $9000 at 12%.
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