I can't figure this out

Question

A business owner has two loans totaling $25,000. The simple interest rates are 7% and 8.5%. If the annual interest charge on the 7% loan is $520 more than on the 8.5% loan, how much did he borrow at each rate?

Answer 1

a + b = 25,000

.07a = .085b + 520

 

Solve the first equation for a or b in order to substitute. Let's solve for a...

 

a = 25,000 - b

 

Now, substitute...

 

.07(25,000 - b) =.085b + 520

1750 - .07b = .085b + 520

-.155b = -1230

b = 7935.48

 

a = 25,000 - 7935.48 = 17064.52

 

Let's check. .07(17064.52) = 1194.52. .085(7935.48) = 674.52. 1194.52 - 674.52 = 520. Check.