SOLUTION: The sum of the first two of three consecutive odd integers is 23 more than the third.

Question 596834: The sum of the first two of three consecutive odd integers is 23 more than the third.
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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To solve this problem we need to translate English phrases into algebraic expressions. Then we write an equation showing the relationship between the integers.
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Let's call the first integer n.
The second integer is n+1 since the two integers are consecutive.
Likewise, the third integer is n+2 because (n+1)+1=n+2.
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We write "the sum of the first two integers" as n+(n+1).
We write "23 more than the third" as (n+2)+23.
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These two expression have the same value, so
[sum of the first two integers] = [23 more than the third]
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Our equation is

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Simplify by combining like terms.

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Subtract n from both sides of the equation to isolate the n-term on the left side.

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Subtract 1 from both sides of the equation to isolate the constant term on the right side.

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We see that the first integer is n=24. Therefore, the other two integers are 25, and 26.
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Always take time to check your work.
Are the first two integers 23 more than the third? 24+25=49 and 49-26=23...Yes!
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That's it! Feel free to email me if this explanation is unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com
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