Question

Kim took out a $55,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 8%, and Bank B charges an interest rate of 11%. After one year, Kim owes $5000 in interest. How much money did she borrow from Bank A?
$20,000
$25,000
$30,000
$35,000

Jack took out a $10,000 loan for a car. He is borrowing money from two banks. Bank A charges an interest rate of 5%, and Bank B charges an interest rate of 6%. After one year, Jack owes $530 in interest. How much money did he borrow from Bank A?

$5000
$6000
$7000
$8000

Answer 1

Kim's Loan:
Let A =  amount borrowed from bank A.
Let B =  amount borrowed from bank B.

The total loan is $55,000.
Therefore
A + B = 55000                  (1)

Bank A charges 8% interest. The interest after 1 year is 0.08A.
Bank B charges 11% interest. The interest after 1 year is 0.11B.
Total interest after 1 year is $5,000.
Therefore
0.08A + 0.11B = 5000      (2)

From (1), obtain
B = 55000 - A                  (3)

Substitute (3) into (2).
0.08A + 0.11(55000 - A) = 5000
0.08A + 6050 - 0.11A = 5000
-0.03A = -1050
A = -1050/-0.03 = 35000

Answer:  Kim borrowed $35,000 from bank A.

Jack's Loan.
A = loan from bank A.
B = loan from bank B.
The total loan is $10,000.
Therefore
A + B = 10000                  (4)

Bank A charges 5% interest and bank B charges 6% interest.
Total interest after 1 year is $530, therefore
0.05A + 0.06B = 530       (5)

From (4), obtain
B = 10000 - A                       (6)

Substitute (6) into (5).
0.05A + 0.06(10000 - A) = 530
0.05A + 600 - 0.06A = 530
-0.01A = -70
A = -70/-0.01 = 7000

Answer: Jack borrowed $7,000 from bank A.