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10 February, 21:19

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

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  1. 10 February, 21:39
    0
    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.
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