SOLUTION: For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?

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Question 226000: For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?
Found 2 solutions by drj, josmiceli:
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?

What is the answer?

Step 1. Let be the first odd integer.

Step 2. Let and and be the next two consecutive integers.

Step 3. Let since the sum of the least and greatest is 146.

Step 4. Solving the equation in Step 3 yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: n=71.
  • Graphical form: Equation was fully solved.
  • Text form: n+n+4=146 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( n+n+4=146 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%29%2An+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-146+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -142
It becomes .
Look at .
Solved linear equation highlight_red%28+2%2An-142=0+%29 equivalent to 2*n-142 =0
It becomes .
Result:
This is an equation! Solutions: n=71.

Universal Simplifier and Solver


Done!



With n=71, then n+2=73 and n+4=75 where the sum of the least and largest number is 146. The sum is 71+73+75=219

Step 8. ANSWER: The sum of the numbers is 219.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV





Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
call the integers ,, and
given:
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