Math Question Simple Interest And System of Equation

Question

Zack borrowed $ 40,000 from 2 money lenders. He paid a simple interest of 12% per annum for one of the loan and 14% per annum for the other. After one year, he paid a total of $ 5,120 as an interest. Let A is the amount borrowed from the first money lender and B is the amount borrowed from the second money lender.

1. Construct the system of equations to illustrate this problem.
2. Determine the amount of money borrowed at each money lender by solving the system of equations.

Answer 1

A + B = 40,000

A = 40,000 - B

.12A + .14B = 5120

.12(40,000-B) + .14B = 5120

(.14-.12)B = 5,120 - 4,800

.02B = 320

B = 320/.02 = 320(50 = $16,000 at 14% earning $2,240 interest

A = 40,000-16,000 = $24,000 at 12% earning $ 2,880 interest

2240+2880 =5120

interest divided by total investment = 5120/40000 = .128 = 12.8 %

12.8 is closer to 12 than to 14. More will be invested at 12% than at 14%

2880>2240