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?
:
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
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total ret: 1755 which is 13% of 13500