Susan invests 2 times as much money at 9% as she does at 5%. If her total interest after 1 year is $1380, how much does she have invested at

Question

Susan invests 2 times as much money at 9% as she does at 5%. If her total interest after 1 year is $1380, how much does she have invested at each rate?

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Eva 2 weeks 2021-09-07T21:33:44+00:00 1 Answer 0

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    2021-09-07T21:34:57+00:00

    Answer: She invested $12000 at 9% and $6000 at 5%

    Step-by-step explanation:

    Let x represent the amount which she invested in the account paying 9% interest.

    Let y represent the amount which she invested in the account paying 5% interest.

    Susan invests 2 times as much money at 9% as she does at 5%.. This means that

    x = 2y

    The formula for determining simple interest is expressed as

    I = PRT/100

    Considering the account paying 9% interest,

    P = $x

    T = 1 year

    R = 9℅

    I = (x × 9 × 1)/100 = 0.09x

    Considering the account paying 5% interest,

    P = $y

    T = 1 year

    R = 5℅

    I = (y × 5 × 1)/100 = 0.05y

    If her total interest after 1 year is $1380, it means that

    0.09x + 0.05y = 1380 – – – – – – – – – -1

    Substituting x = 2y into equation 1, it becomes

    0.09 × 2y + 0.05y = 1380

    0.18y + 0.05y = 1380

    0.23y = 1380

    y = 1380/0.23

    y = 6000

    x = 2y = 2 × 6000

    x = 12000

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