the total value of two investments is $5,000. The average annual interest rate for one investment is 10% and 14% for the other. The total annual interest is $620. How much is invested at each rate?

Let the amount invested at 10% =M Then, the amount invested at 14% =5,000 - M

0.10M + 0.14[5,000 - M] =620 0.10M + 700 - 0.14M =620 - 0.04M = 620 - 700 =- 80 M = - 80 / - 0.04

M =$2,000 invested at 10% $5,000 - $2,000 =$3,000 invested at 14%