SOLUTION: If one-half of a number is added to one-third of the next consecutive number, the sum is 67. What are the two numbers?

Question 85407: If one-half of a number is added to one-third of the next consecutive number, the sum is 67. What are the two numbers?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If x is the unknown number, then the next consecutive number is x + 1.
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If one-half of the unknown number (that is (1/2)*x) is added to one-third of the next
consecutive number (that is (1/3)*(x + 1)) the sum is 67.
.
In equation form this can be written as:
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(1/2)*x + (1/3)*(x + 1) = 67
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Multiply out the distributed multiplication on the left side to get:
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(1/2)*x + (1/3)*x + (1/3) = 67
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Get rid of the denominators by multiplying everything in this equation by the common
denominator of 2*3 or 6. If you multiply all the terms by 6 the result is:
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(6/2)*x + (6/3)*x + (6/3) = 67 * 6
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which simplifies to:
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3*x + 2*x + 2 = 402
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The x terms can be added together to get:
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5*x + 2 = 402
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Subtract 2 from both sides:
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5*x = 400
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Divide both sides by 5 and you get:
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x = 80
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that means that the next consecutive integer is 81. So the two numbers are 80 and 81.
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Check:
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Does one-half of 80 when added to one-third of 81 = 67?
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One-half of 80 is 40 and one-third of 81 is 27. Adding 40 and 27 does result in 67, so
the two numbers 80 and 81 do satisfy the problem.
.
Hope this helps.
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