SOLUTION: find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number

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Question 222441: find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number.

Step 1. Let n be an integer.

Step 2. Let n+1 and n+2 be the next two consecutive integers.

Step 3. Let n+n+1=2n+1 be the sum of the two smallest integers.

Step 4. Let 2(2n+1) be twice the sum of the two smallest integers.

Step 5. Let 3(n+2) be three times the largest number

Step 6. Then using Steps 3 and 4, 2(2n+1)=3(n+2)+10 since twice the sum of the two smallest numbers is 10 more than three times the largest number.

Step 7. Solving yields the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: n=14.
  • Graphical form: Equation 2%2A%282n%2B1%29=3%2A%28n%2B2%29%2B10 was fully solved.
  • Text form: 2*(2n+1)=3*(n+2)+10 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%282n%2B1%29=3%2A%28n%2B2%29%2B10+%29
    For tutors: simplify_cartoon( 2*(2n+1)=3*(n+2)+10 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%282%2An%2B1%29=highlight_red%28+3%2A%28n%2B2%29%2B10+%29.
Moved these terms to the left highlight_green%28+-3%2A%28n%2B2%29+%29,highlight_green%28+-10+%29
It becomes 2%2A%282%2An%2B1%29-highlight_green%28+3%2A%28n%2B2%29+%29-highlight_green%28+10+%29=0.
Look at highlight_red%28+2%2A%282%2An%2B1%29+%29-3%2A%28n%2B2%29-10=0.
Expanded term 2 by using associative property on %282%2An%2B1%29
It becomes highlight_green%28+2%2A2%2An+%29%2Bhighlight_green%28+2%2A1+%29-3%2A%28n%2B2%29-10=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2An%2B2%2A1-3%2A%28n%2B2%29-10=0.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2An%2B2%2A1-3%2A%28n%2B2%29-10=0.
Look at 4%2An%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29-3%2A%28n%2B2%29-10=0.
Multiplied numerator integers
It becomes 4%2An%2Bhighlight_green%28+2+%29-3%2A%28n%2B2%29-10=0.
Look at 4%2An%2Bhighlight_red%28+2+%29-3%2A%28n%2B2%29-highlight_red%28+10+%29=0.
Added fractions or integers together
It becomes 4%2An%2Bhighlight_green%28+-8+%29-3%2A%28n%2B2%29=0.
Look at 4%2An%2Bhighlight_red%28+-8+%29-3%2A%28n%2B2%29=0.
Moved -8 to the right of expression
It becomes 4%2An-3%2A%28n%2B2%29%2Bhighlight_green%28+-8+%29=0.
Look at 4%2An-3%2A%28n%2B2%29%2Bhighlight_red%28+-8+%29=0.
Removed extra sign in front of -8
It becomes 4%2An-3%2A%28n%2B2%29-highlight_green%28+8+%29=0.
Look at 4%2An-highlight_red%28+3%2A%28n%2B2%29+%29-8=0.
Expanded term -3 by using associative property on %28n%2B2%29
It becomes 4%2An-highlight_green%28+3%2An+%29-highlight_green%28+3%2A2+%29-8=0.
Look at 4%2An-3%2An-highlight_red%28+3+%29%2Ahighlight_red%28+2+%29-8=0.
Multiplied numerator integers
It becomes 4%2An-3%2An-highlight_green%28+6+%29-8=0.
Look at 4%2An-3%2An-highlight_red%28+6+%29-highlight_red%28+8+%29=0.
Added fractions or integers together
It becomes 4%2An-3%2An%2Bhighlight_green%28+-14+%29=0.
Look at 4%2An-3%2An%2Bhighlight_red%28+-14+%29=0.
Removed extra sign in front of -14
It becomes 4%2An-3%2An-highlight_green%28+14+%29=0.
Look at highlight_red%28+4%2An+%29-highlight_red%28+3%2An+%29-14=0.
Eliminated similar terms highlight_red%28+4%2An+%29,highlight_red%28+-3%2An+%29 replacing them with highlight_green%28+%284-3%29%2An+%29
It becomes highlight_green%28+%284-3%29%2An+%29-14=0.
Look at highlight_red%28+%284-3%29+%29%2An-14=0.
Remove extraneous '1' from product highlight_red%28+%284-3%29+%29
It becomes n-14=0.
Look at highlight_red%28+n-14+%29=0.
Solved linear equation highlight_red%28+n-14=0+%29 equivalent to n-14 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=14.

Universal Simplifier and Solver


Done!



n=14, then n+1=15 and n+2=16

Check original equation 2%282n%2B1%29=3%28n%2B2%29%2B10 or 2%2814%2B15%29=3%2A16%2B10 such that 58=58 which is a true statement.

Step 8. ANSWER: The three consecutive integers are 14, 15, and 16.

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.

Good luck in your studies!

Respectfully,
Dr J


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.

Good luck in your studies!

Respectfully,
Dr J