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

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