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

Algebra ->  Real-numbers -> SOLUTION: For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?      Log On


   

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) About Me  (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 n be the first odd integer.

Step 2. Let n%2B2 and n%2B4 and be the next two consecutive integers.

Step 3. Let n%2Bn%2B4=146 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 n%2Bn%2B4=146 was fully solved.
  • Text form: n+n+4=146 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B4=146+%29
    For tutors: simplify_cartoon( n+n+4=146 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B4=146.
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 highlight_green%28+%281%2B1%29%2An+%29%2B4=146.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B4=146.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2An%2B4=146.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B4=146.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2An%2B4=146.
Look at 2%2An%2B4=highlight_red%28+146+%29.
Moved these terms to the left highlight_green%28+-146+%29
It becomes 2%2An%2B4-highlight_green%28+146+%29=0.
Look at 2%2An%2Bhighlight_red%28+4+%29-highlight_red%28+146+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+-142+%29=0.
Look at 2%2An%2Bhighlight_red%28+-142+%29=0.
Removed extra sign in front of -142
It becomes 2%2An-highlight_green%28+142+%29=0.
Look at highlight_red%28+2%2An-142+%29=0.
Solved linear equation highlight_red%28+2%2An-142=0+%29 equivalent to 2*n-142 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
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) About Me  (Show Source):
You can put this solution on YOUR website!
call the integers n,n%2B1, and n%2B2
given:
n+%2B+n%2B2+=+146
2n+%2B+2+=+146
2n+=+144
n+=+72
n%2B1+=+73
n%2B2+=+74
72%2B73%2B74+=+219