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? Please show work

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Mary 2 weeks 2022-01-11T15:21:27+00:00 1 Answer 0 views 0

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    2022-01-11T15:22:53+00:00

    William had $37.5 and Gracie had $52.5 in the beginning

    Step-by-step explanation:

    William says to Gracie:

    • “If you give me $7.50, we will have an 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”

    Assume that William has $x and Gracie has $y at the beginning

    ∵ William has $x

    ∵ Gracie has $y

    ∵ When Gracie gives William $7.5, they will have the same

       amount of money

    – That means subtract 7.5 from Gracie and add 7.5 to William

       and equate the two answers

    ∴ x + 7.5 = y – 7.5

    – Subtract 7.5 from both sides

    x = y – 15 ⇒ (1)

    ∵ When William gives Gracie $7.5, Gracie will have twice as

       much money as William

    – That means add 7.5 to Gracie and equate the sum

      by 2 times the difference of William and 7.5

    ∴ y + 7.5 = 2(x – 7.5)

    ∴ y + 7.5 = 2x – 15

    – Subtract 7.5 from both sides

    y = 2x – 22.5 ⇒ (2)

    Now we have system of equations to solve it

    Substitute y in equation (1) by equation (2)

    ∵ x = 2x – 22.5 – 15

    – Add the like terms in the right hand side

    ∴ x = 2x – 37.5

    – Subtract 2x from both sides

    ∴ – x = -37.5

    – Divide both sides by -1

    x = 37.5

    – Substitute the value of x in equation (2) to find y

    ∵ y = 2(37.5) – 22.5

    y = 52.5

    William had $37.5 and Gracie had $52.5 in the beginning

    Learn more:

    You can learn more about the system of equations in brainly.com/question/2115716

    #LearnwithBrainly

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