Question 112957
If the first integer is x, then the next consecutive integer is x+1.
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The problem tells you to find one-half of the first integer and subtract it from three-fifths 
of the second integer.
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Since the first integer is x, one-half of that integer is {{{x/2}}}.
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And since the second integer is x+1, then three fifths of that integer is:
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{{{(3/5)*(x + 1)}}} which is equivalent to {{{(3*(x+1))/5}}}
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Subtract the first from the second and you have a difference of:
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{{{(3*(x+1))/5 - x/2}}}
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Finally, the problem tells you that this difference is equal to 3. So you can write this
in equation form as:
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{{{(3*(x+1))/5 - x/2 = 3}}}
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You can get rid of the denominator 5 by multiplying all terms on both sides of this equation
by 5 and the result is:
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{{{3*(x+1) -(5x)/2 = 15}}}
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Next you can get rid of the denominator 2 by multiplying all terms on both sides of this
equation by 2 and the result is:
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{{{2*3*(x+1) - 5x = 30}}}
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Multiply the 2 times 3 and the equation reduces to:
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{{{6*(x+1) - 5x = 30}}}
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Now do the distributed multiplication on the left side by multiplying 6 times both of the
terms in the parentheses to make the equation become:
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{{{6x + 6 - 5x = 30}}}
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Combine the 6x and -5x and the equation becomes:
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{{{x + 6 = 30}}}
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Get rid of the 6 on the left side by subtracting 6 from both sides to reduce the equation to:
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{{{x = 24}}}
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This tells you that one of the integers is 24. Then next consecutive integer must be 25.
So the two numbers you were looking for are 24 and 25.
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Check. Half of 24 is 12. And three-fifths of 25 is 15. Subtract 12 from 15 and the answer
is 3 ... just as the problem said it should be. Therefore, the answer is correct.
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Hope this helps you to understand the problem and how you can solve it.