Question

Stefan borrowed twice as much on his 8 % car loan as on his 7% student loan. The annual interest

on the car loan is $360 more than the interest on the student loan. How much did Stefan borrow on
each loan?
a. Write an equation about the principals on the loans, using for the amount of money he borrowed
for his car and y for the amount of money he borrowed for his student loan.
b. Write another equation about the interest on the loans.
c. Solve your system and answer the question for much he borrowed at each rate.
Car: $
Student: $

Answer 1

Stefan borrowed $8000 on his car loan and $4000 on his student loan.

Explanation:

a. Let x be the amount of money Stefan borrowed on his car loan and y be the amount he borrowed on his student loan. According to the problem, Stefan borrowed twice as much on his car loan as on his student loan, so x = 2y.

b. The annual interest on the car loan is $360 more than the interest on the student loan. We can set up an equation as follows:

0.08x - 0.07y = 360

c. Substituting x = 2y from equation (a) into equation (b), we get:

0.08(2y) - 0.07y = 360

0.16y - 0.07y = 360

0.09y = 360

y = 4000

So, Stefan borrowed $4000 on his student loan. Using equation (a), we can find the amount he borrowed on his car loan:

x = 2y = 2(4000) = 8000

Therefore, Stefan borrowed $8000 on his car loan and $4000 on his student loan.