interest at two different rates

Question

If Ben invests $4,000 at 4% interest per year how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5% of the total amount invested

Answer 1

4% = 0.04

5.5% = 0.055

 

0.04 * 4000 + 0.055 * X = 0.045 * (X + 4000)

 

160 + 0.055X = 0.045X + 180

 

160 +   0.055X - 0.045X - 180 = 0

 

0.01X - 20 = 0

 

0.01X = 20

 

X = 2000

 

Check: 0.04*4000 + 0.055*2000 = 270 and 270/6000 = 0.045 = 4.5%

 

  and 1710 / (4000 + 2000) = 1710 / 6000