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

Question

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?

Answer 1

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.

Answer 2

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 :)

Answer 3

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%