SOLUTION: 1.if one-third of an integer is added to one-half of the next consecutive integer, the difference is 3. What are the two integers?

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Question 53600: 1.if one-third of an integer is added to one-half of the next consecutive integer, the difference is 3. What are the two integers?


Found 2 solutions by stanbon, rchill:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if one-third of an integer is added to one-half of the next consecutive integer, the difference is 3. What are the two integers?
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Let the 1st integer be "x".
The next consecutive integer is "x+1".
Now you need an equation.
But your word statement says "added" and then says "difference".
You can't have it both ways.
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.