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?

Answer: 32

Step-By-Step: 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:

+x+-+18+=+2%28x+-+25%29 + (the amount of money Lily has now = two times the amount of money Sara has now)

Now we solve for x:

+x+-+18+=+2x+-+50 + (distribute the 2 on the right hand side)

+-18+=+x+-+50 + (subtract x from both sides)

+32+=+x + (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.