Write a system of equations to model this situation Solve us

Write a system of equations to model this situation. Solve using substitution or eliminationYou borrow a total of $5500 in student loans from two lenders. One charges 3.8% simple interest and the other charges 5.8% simple interest. You don\'t have to start making payments on either loan for 3 years. When you begin making payments you owe a total of $855 in interest. How much did you borrow from each lender?

Solution

You borrow a total of 5500

Say you borrow x from the person that charges 3.8%
So, you borrow y from the one that charges 5.8%

So, x + y = 5500

Interest on x at 3.8% over 3 years= x*0.038*3 = 0.114x
Interest on y at 5.8% over 3 yrs = y*0.058*3 = 0.174y

So, now, total interest = 855

0.114x + 0.174y = 855

Using substitution :

0.114x + 0.174(5500 - x) = 855

0.114x + 957 - 0.174x = 855

-0.06x = -102

x = 1700

So, y = 5500 - 1700 ---> y = 3800

So, you borrow 1700 at 3.8% ---> ANSWER
And 3800 at 5.8% ---> ANSWER