Algebra

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an investment of 72,000 was made by a business club. the investment was split into three parts and lasted for one year. the first part of the investment earned 8% interest. the second 6% and the third 9%. total interest from the investments was $5640. the interest from the first investment was 3 times the interest from the second. find the amounts of three parts of the investment

  • Algebra -

    $X-in 1st inv.
    $Y-in 2nd inv.
    $Z-in 3rd inv.

    0.08X + 0.06Y + 0.09Z = $5640.

    Eq1: 0.08X + 0.06Y + 0.09Z = 5640.
    Eq2: X + Y + Z = 72000.
    Multiply Eq1 by 100 and Eq2 by -9:
    8X + 6Y + 9Z = 564000,
    -9X - 9Y - 9Z = - 648000,
    Add the Eqs:
    -X - 3Y = -84,000,

    0.08X = 3*0.06Y,
    X = 2.25Y
    Substitute 2.25Y for X:
    -2.25Y - 3Y = -84000,
    -5.25Y = -84000,

    Y = $16000.

    X = 2.25Y = 2.25 * 16000 = $36,000.

    X + Y + Z = $72000,
    36000 + 16000 + Z = 72000,

    Z = $20,000.

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