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How much money would Garrett have to invest at 10% so that that combined interest rate for both investments was 7% over the year?

This the complete question I need help with:
Garrett invested $12,000 at an annual interest rate of 6%. How much money would Garrett have to invest at 10% so that that combined interest rate for both investments was 7% over the year?
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3 Answers

The unknown x is how much to invest at 10%.
 
The combined amount being invested is $12,000 + x and you want the combined rate to be 7%
 
Write that as 1.07 (12,000 + x)
 
The individual investments are 1.06 (12,000) and 1.10 (x)
 
Add the individual investments together and set them equal to the combined investment and solve for x
 
1.06 (12,000) + 1.1 (x) = 1.07 (12,000 + x)
 
12,720 + 1.1x = 12840 + 1.07x
 
.03x = 120
 
x = $4000 is invested at 10%
 
You can check by plugging back in.
Hey Enileda -- here's another angle on "mixtures" ... the "spread" is 4% from 6 to 10
 
... we wish to move 1/4 thru that spread to 7% ... needing a 3:1 mix heavy at the 6% end
 
==> 3:1 mix means a $12k to $4k mix ... Best wishes :)
x= amount invested at 10 %
 
12,000(0.06)+x(0.10)=(12000+x)(0.07)
720+0.1x=840+0.07x
0.1x-0.07x=840-720
0.03x=120
3x=12,000
x=$4000
check: $12,000+$4000=$16,000
$720+$400(10% of $4000)=$1120
1120/16,000=0.07=7%