Interest rate percentage

Question

Phyllis invested $11,000, a portion earning a simple interest rate of 4 1/5% per year and the rest earning a rate of 4% per year. After 1 year the total interest earned on these investments was $457. How much money did she invest at each rate?

Answer 1

a + b = 11,000

0.045a + 0.04b = 457

 

a = 11,000 - b

 

0.045(11,000 - b) + 0.04b = 457

495 - 0.045b + 0.04b = 457

-0.005b = 38

b = 7600

 

a = 11,000 - b

a = 11,000 - 7600

a = 3400