A person invested $7900 for one year, part at 5%, part at 11%, and the remainder at 15%. The total annual income from these investments was $965. The amount of money invested at 15% was $500 more than the amounts invested at 5% and 11% combined. Find the amount invested at each rate.

Answer 1

x+y+z = 7900
.05x + .11y + .15z = 965
z = x+y + 500