document.write( "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?\r
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Algebra.Com's Answer #35851 by rchill(405) $\"\"$ $\"About$

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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. \n" ); document.write( "

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