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14 October, 00:43

An actor invests some money at 9 % simple interest, and $24,000 more than three times the amount at 10 % simple interest. The total annual interest earned from the investment is $38,670. How much did he invest at each amount? Use the six-step method.

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  1. 14 October, 02:00
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    The amount invested at 9% is $93000

    The amount invested at 10% is $303000

    Step-by-step explanation:

    Let the amount invested at 9% interest rate be x

    And the amount invested at 10% rate be y

    Simple Interest from x in a year = 0.09x

    Simple Interest from y in a year = 0.1y

    But y = 24000 + 3x

    And the sun of the interests, 0.09x + 0.1y = 38670

    Now we have a simultaneous eqn

    y = 24000 + 3x (eqn 1)

    0.09x + 0.1y = 38670 (eqn)

    Substitute y into eqn 2

    0.09x + 0.1 (24000 + 3x) = 38670

    0.09x + 2400 + 0.3x = 38670

    0.39x = 38670 - 2400

    x = 36270/0.39 = $93000

    y = 24000 + 3x = 24000 + 3 * 93000 = $303000
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