William says to Gracie, “If you give me $7.50,we will have and equal amount of money. “Grace responds, “That may be true, but if you give me

Question

William says to Gracie, “If you give me $7.50,we will have and equal amount of money. “Grace responds, “That may be true, but if you give me $ 7.50 instead, I will have twice as much money as you. “How much money did William and Grace each have in the beginning?

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Luna 2 weeks 2022-01-11T14:03:57+00:00 1 Answer 0 views 0

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    2022-01-11T14:05:30+00:00

    Answer:

    The amount that William has at the beginning is $37.50 and the amount that Gracie has at the beginning is $52.50

    Step-by-step explanation:

    Let

    x —> amount that William has at the beginning

    y —> amount that Gracie has at the beginning

    we know that

    William says to Gracie, “If you give me $7.50,we will have and equal amount of money

    so

    x+7.50=y-7.50

    y=x+15.00 —-> equation A

    “Grace responds, if you give me $ 7.50 instead, I will have twice as much money as you

    2(x-7.50)=(y+7.50)

    2x-15.00=y+7.50

    2x-y=22.50 —-> equation B

    substitute equation A in equation B

    2x-(x+15.00)=22.50

    solve for x

    x=22.50+15.00=37.50

    Find the value of y

    y=37.50+15.00=52.50

    therefore

    The amount that William has at the beginning is $37.50 and the amount that Gracie has at the beginning is $52.50

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