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

Answer 1

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

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