SOLUTION: If one-half of ane integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?

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Question 53607: If one-half of ane integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?
Found 2 solutions by stanbon, rchill:
Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
If one-half of ane integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?
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Consecutive integers are x and x+1.
EQUATION:
(3/5)(x+1)-(1/2)x = 3
Multiply thru by 10 to get:
3(x+1)-5x = 30
-2x=27
x=-27/2
Cheers,
Stan H.

Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the first integer; then x+1 is the next consecutive integer. The equation is %283%2F5%29%2A%28x%2B1%29-%281%2F2%29x=3. Expanding gives us %283%28x%2B1%29%29%2F5-x%2F2=3. Now multiply both sides by 10 to get 6%28x%2B1%29-5x=30. Expanding gives us 6x%2B6-5x=30, which further simplifies to x%2B6=30. Subtracting 6 from both sides give us x=24. That means that our two integers are 24 and 25. Taking one-half of 24 gives us 12; taking three-fifths of 25 gives us 15. The difference between 15 and 12 is 3, so we just proved our answer is correct.