Interest rate word question

Question

Laura borrowed a total of 

$23,000

 from two different banks to start a business. One bank charged the equivalent of 4%

 simple interest, and the other charged 5.5%

 interest. If the total interest after 2

 years was $1930

, determine the amount borrowed from each bank.

Let x represent the principal on the business loan at 4%

Then ___ is the reamaining amount borrowed at 5.5%

Answer 1

Let a = fraction of money invested at 4% and b = fraction of money invested at 5.5%

Then 23000a(1.04)² + 23000b(1.055)² = 24930 (That is after 2 years this is total money from both investments including the original principal). Simplifying we get

24876.8a + 25599.575b = 24930 also

a + b = 1

Solving for a & b from both equations, we find a = .9264 and b = .0736

So, 23000(.9264) = 21,307.20 was invested at 4% and

23000(.0736) = 1692.80 was invested at 5.5%