Question

Garret invested $12,000 at an annual interest rate of 6%. How much money would Garret have had to invest at 10% so that the combined interest rate for both investments was 7% over the year?

Answer 1

Garrett would have to invest 4000 at 10%

Answer 2

Explanation:

To determine how much money Garret would have had to invest at 10% in order to achieve a combined interest rate of 7% over the year, we can set up the following equation:

(12000 * 0.06) + (x * 0.10) = (12000 + x) * 0.07

Let's solve this equation to find the value of 'x', which represents the amount Garret would have had to invest at 10%:

720 + 0.10x = 0.07(12000 + x)

Simplifying the equation:

720 + 0.10x = 840 + 0.07x

0.10x - 0.07x = 840 - 720

0.03x = 120

x = 120 / 0.03

x = 4000

Therefore, Garret would have had to invest $4,000 at a 10% annual interest rate in order to achieve a combined interest rate of 7% over the year.