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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?

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%