SOLUTION: find the three consecutive odd integers such that the sum of the first two odd integers exceeds the third by 9.

Question 213912: find the three consecutive odd integers such that the sum of the first two odd integers exceeds the third by 9.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Find the three consecutive odd integers such that the sum of the first two odd integers exceeds the third by 9.

Step 1. Let n be an odd integer, n+2 and n+4 be the next two consecutive odd integers.

Step 2. Let n+n+2 is the sum of the first two integers

Step 3. Then, n+n+2=n+4+9 Since the sum of n+n+2 is 9 more than the third integer given as n+4

Step 4. Solve the above equation using the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

This is an equation! Solutions: n=11.
Graphical form: Equation was fully solved.
Text form: n+n+2=n+4+9 simplifies to 0=0
Cartoon (animation) form:
For tutors: simplify_cartoon( n+n+2=n+4+9 )
If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+n+%29

replacing them with highlight_green%28+%281%2B1%29%2An+%29

It becomes .

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Added fractions or integers together
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Remove unneeded parentheses around factor highlight_red%28+2+%29

It becomes .

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Added fractions or integers together
It becomes .

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Moved these terms to the left highlight_green%28+-n+%29

It becomes .

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Added fractions or integers together
It becomes .

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Moved

to the right of expression
It becomes .

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Removed extra sign in front of

It becomes .

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Eliminated similar terms highlight_red%28+2%2An+%29

replacing them with highlight_green%28+%282-1%29%2An+%29

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Remove extraneous '1' from product highlight_red%28+%282-1%29+%29

It becomes .

Look at .
Solved linear equation highlight_red%28+n-11=0+%29

equivalent to n-11 =0
It becomes .
Result:
This is an equation! Solutions: n=11.

Universal Simplifier and Solver

Done!

Step 5. ANSWER: So the integers are 11, 13 and 15.

Check 11+13=24 which is 9 more than 15. So it checks!

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

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