Question 883148: William says to Gracie, "If you give me $5.50, we will have an equal amount of money." Gracie responds, "That may be true, but if you give me $5.50 instead, I will have twice as much money as you." How much money did William and Gracie each have in the beginning?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! William says to Gracie, "If you give me $5.50, we will have an equal amount of money."
Gracie responds, "That may be true, but if you give me $5.50 instead, I will have twice as much money as you."
How much money did William and Gracie each have in the beginning?
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Let w = W's original amt
Let g = G's original amt
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Write an equation for each statement, simplify as much as possible.
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"William says to Gracie, "If you give me $5.50, we will have an equal amount of money."
w + 5.50 = g - 5.50
w = g - 5.50 - 5.50
w = g - 11
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Gracie responds, "That may be true, but if you give me $5.50 instead, I will have twice as much money as you"
g + 5.50 = 2(w-5.50)
g + 5.50 = 2w - 11
g - 2w = -11 - 5.50
g - 2w = -16.50
replace w with (g-11)
g -2(g-11) = -16.50
g - 2g + 22 - 16.50
-g = 16.50 - 22
-g = -38.50
g = 38.50 is G's original amt
find w
w = 38.50 - 11
w = 27.50 is W's original amt
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You can confirm this for yourself, try these value in both statements
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