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

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.