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13 December, 11:32

A business has two loans totaling $85,000. One loan has a rate of 4.5% and the other has a rate of 6%. This year, the business expects to pay $4,650 in interest on the two loans. How much is each loan?

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  1. 13 December, 11:56
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    Answer: Loan a:$30,000, Loan b:$55,000

    Step-by-step explanation:

    We have to loans, loan a and loan b, and both sum to $85,000:

    a + b=$85,000 (1)

    On the other hand, we know loan a has a rate of 4.5%=0.045 and loan b has a rate of 6%=0.06:

    0.045 a + 0.06 b=$4,650 (2)

    So, we have a system with two equations to solve:

    Isolating a from (1):

    a=$85,000 - b (3)

    Substituting (3) in (2):

    0.045 ($85,000 - b) + 0.06 b=$4,650 (4)

    b=$55,000 (5) This is loan b

    Substituting (5) in (1):

    a + $55,000=$85,000 (6)

    a = $30,000 (7) This is loan a
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