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algebra

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Select the set of equations that represents the following situation: Mary invested one amount at 7% simple interest, and a second amount at 5% interest, earning $29.80 in one year. If she had switched the amounts, she would have earned $35.00. What were the two amounts?

  • algebra -

    Invested $X @ 7%.
    Invested $Y @ 5%.

    Eq1: 0.07X + 0.05Y = $29.80.
    Eq2: 0.05X + 0.07Y=35(Amountswitched).
    Multiply both Eqs by 100:
    7X + 5Y = 2980
    5X + 7Y = 3500
    Multiply 1st Eq by -5 and 2nd Eq by7:
    -35X -25Y = -14900
    35X + 49Y = 24500
    Add the 2 Eqs and get:
    24Y = 9600,
    Y = $400.

    Substitute 400 for Y in Eq2:
    0.05X + 0.07*400 = 35,
    0.05X + 28 = 35,
    0.05X = 35 - 28 = 7,
    X = 7 / 0.05 = $140.

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