SOLUTION: Lily and Sara each had an equal amount of money at first. After Lily spent $18 and Sara spent $25. Lily had twice as much as Sara. How much money did each have at first? I dont

Question 514024: Lily and Sara each had an equal amount of money at first. After Lily spent $18 and Sara spent $25. Lily had twice as much as Sara. How much money did each have at first?
I dont know how to complete this problem.
I was thinking:
Lily = x-18y=36
Sara= x-25y=
Then I am stuck.....
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
You started on the right track, but you actually only need one variable. Let x be the amount of money both Lily and Sara have at first. We have a relationship in words between the amount of money Lily and Sara have now, and we need to convert this relationship into an algebraic equation. First, Lily spent $18, so the amount of money Lily has now is x - 18. Sara spent $25, so likewise the amount of money Sara has now is x - 25. We know that Lily now has twice as much money as Sara, so we can write this fact algebraically as:
(the amount of money Lily has now = two times the amount of money Sara has now)
Now we solve for x:
(distribute the 2 on the right hand side)
(subtract x from both sides)
(add 50 to both sides)
So we got x = 32. Does this make sense? If both Lily and Sara started with $32, Lily would now have $32 - $18 = $14, while Sara would now have $32 - $25 = $7, so Lily would now have twice as much money as Sara. Thus $32 is the answer.
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