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
[tex]x+7.50=y-7.50[/tex]
[tex]y=x+15.00[/tex] ----> equation A
"Grace responds, if you give me $ 7.50 instead, I will have twice as much money as you
[tex]2(x-7.50)=(y+7.50)[/tex]
[tex]2x-15.00=y+7.50[/tex]
[tex]2x-y=22.50[/tex] ----> equation B
substitute equation A in equation B
[tex]2x-(x+15.00)=22.50[/tex]
solve for x
[tex]x=22.50+15.00=37.50[/tex]
Find the value of y
[tex]y=37.50+15.00=52.50[/tex]
therefore
The amount that William has at the beginning is $37.50 and the amount that Gracie has at the beginning is $52.50
