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?
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
