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Amanda invested a total of $3 comma 100 into three separate accounts that pay 4 % , 6 % and 7 % annual interest. Amanda has three times as much invested in the account that pays 7 % as she does in the account that pays 4 %. If the total interest for the year is $ 191 comma how much did Amanda invest at each rate?

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  1. Today, 09:22
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    the amount invested at 4% interest is $5,00

    the amount invested at 6% interest is $1,100

    the amount invested at 7% interest is $1,500

    Explanation:

    Data provided in the question:

    Total amount invested = $3,100

    Interest rates : 4% , 6 % and 7 %

    Total interest = $191

    Now,

    Let the amount invested at 4% interest be 'x'

    the amount invested at 6% interest be 'y'

    the amount invested at 7% interest be 'z'

    Therefore,

    According to the question:

    x + y + z = $3,100 ... (1)

    z = 3x ... (2)

    0.04x + 0.06y + 0.07z = $191 ... (3)

    From (1) and (2), we have

    x + y + 3x = $3,100

    or

    4x + y = $3,100

    or

    y = $3,100 - 4x, ... (4)

    from 2, 3 and 4, we have

    0.04x + 0.06 ($3,100 - 4x) + 0.07 (3x) = $191

    ⇒ 0.04x + 186 - 0.24x + 0.21x = $191

    ⇒ 0.01x + 186 = $191

    ⇒ 0.01x = 5

    or

    x = $500

    thus,

    from (2)

    z = 3 * 500

    or

    z = $1,500

    From (4)

    y = $3,100 - 4 (500)

    or

    y = $1,100

    Hence,

    Amanda invested

    the amount invested at 4% interest is $5,00

    the amount invested at 6% interest is $1,100

    the amount invested at 7% interest is $1,500
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