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?

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) (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) (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 . Expanding gives us . Now multiply both sides by 10 to get . Expanding gives us , which further simplifies to . Subtracting 6 from both sides give us . 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.
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