Question 972560
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Let x=number of Tom's oranges
When Stacy asked Tom how many oranges he had. Tom replied, " If I had as many more (x+x) and half as many more (x+x+(1/2)x) and one and one-half oranges (2.5x+1.5), I'd have 34. How many oranges does Tom have? 
2.5x+1.5=34
2.5x=32.5
x=13 Tom has 13 oranges.
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I don't know of an elegant way to solve this type of problem, just work from the end to the beginning:
Barrel X (88 L) contains more cider than barrel Y (40 L). From barrel X pour into Y as much cider as Y already contains.(Now X=48 L and Y=80 L) Then from Y pour (48 L) into X as much cider as X now contains (48 L).(Now X=96 L and y=32 L) Finally, Pour (32 L) from X (After pouring X has 64 L) into Y as much cider as Y presently has (32 L). Now both barrels contain 64 liters of cider. How many liters of cider did each barrel contain before the pouring process began.