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16 October, 01:44

A bank loaned out $17,000 , part of it at the rate of 9 % per year and the rest at 17 % per year. If the interest received in one year totaled $2,000 , how much was loaned at 9 %? How much of the $17,000 did the bank loan out at 6%?

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  1. 16 October, 01:54
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    1) bank loaned at 9% = $11,066

    2) bank loaned at 17% = $5,934

    3) bank loaned at 6% = $1,020

    Step-by-step explanation:

    Step 1:

    assume;

    1) x is the amount loaned for 9%

    2) y is the amount loaned for 17%

    3) z is the internet amount received after one year = $2,000

    4) A is total amount loaned = $17,000

    Step 2:

    bank loaned $17,000 for 9% and 17% interest therefor;

    A=X+Y

    17000 = X + Y

    For X;

    X=17000-Y

    Step 3:

    Interest received at the end of one year will be;

    Z = (X*9%) + (Y*17%)

    2000 = X (9/100) + Y (17/100)

    2000 = X (0.09) + Y (0.17)

    For X;

    X (0.09) = 2000-0.17Y

    X = (2000-0.17Y) / 0.09

    X = (2000/0.09) - (0.17/0.09) Y

    X = 22,222 - 1.88Y

    Step 4:

    We have two values of X from Step 2 and 3, now compare both;

    17000-Y = 22,222 - 1.88Y

    For Y

    1.88Y - Y = 22,222-17,000

    0.88Y = 5,222

    Y = 5,222/0.88

    Y = $5,934

    Step 5:

    For X;

    X=17,000-Y

    X = 17,000-5,934

    X = $11,066

    Step 6:

    For last question that is how much bank loaned for 6%, assume it is B;

    B = 17,000 * 6%

    B = 17,000 * (6/100)

    B = 17,000 * 0.06

    B = $1,020
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