SOLUTION: Find two consecutive even integers such that three times the lesser integer, added to the larger integer, is 58.

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Question 214097: Find two consecutive even integers such that three times the lesser integer, added to the larger integer, is 58.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find two consecutive even integers such that three times the lesser integer, added to the larger integer, is 58.

Step 1. Let n be an even integer and n+2 be the next consecutive even integer

Step 2. 3n be three times the lesser integer

Step 3. 3n+n+2 be three times the lesser integer added to the larger integer n+2

Step 4. 3n+n+2=58 be three times the less integer added to the larger integer n+2 is 58.

Step 5. The following steps will solve the equation 3n+n+2=58.

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


YOUR ANSWER


  • This is an equation! Solutions: n=14.
  • Graphical form: Equation 3n%2Bn%2B2=58 was fully solved.
  • Text form: 3n+n+2=58 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3n%2Bn%2B2=58+%29
    For tutors: simplify_cartoon( 3n+n+2=58 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+3%2An+%29%2Bhighlight_red%28+n+%29%2B2=58.
Eliminated similar terms highlight_red%28+3%2An+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%283%2B1%29%2An+%29
It becomes highlight_green%28+%283%2B1%29%2An+%29%2B2=58.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+1+%29%29%2An%2B2=58.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2An%2B2=58.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2An+%29%2B2=58.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2An%2B2=58.
Look at 4%2An%2B2=highlight_red%28+58+%29.
Moved these terms to the left highlight_green%28+-58+%29
It becomes 4%2An%2B2-highlight_green%28+58+%29=0.
Look at 4%2An%2Bhighlight_red%28+2+%29-highlight_red%28+58+%29=0.
Added fractions or integers together
It becomes 4%2An%2Bhighlight_green%28+-56+%29=0.
Look at 4%2An%2Bhighlight_red%28+-56+%29=0.
Removed extra sign in front of -56
It becomes 4%2An-highlight_green%28+56+%29=0.
Look at highlight_red%28+4%2An-56+%29=0.
Solved linear equation highlight_red%28+4%2An-56=0+%29 equivalent to 4*n-56 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=14.

Universal Simplifier and Solver


Done!


Then n+2=16 when n=14

Check 3*14+16=58. So it works!!

Step 6. ANSWER: The integers are 14 and 16.

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