SOLUTION: the product of two consec. pos. intergers is 29 more than thier sum. find the intergers.

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Question 214195: the product of two consec. pos. intergers is 29 more than thier sum. find the intergers.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The product of two consecutive positive integers is 29 more than their sum. find the integers.

Step 1. Let n be one positive integer and n+1 is the next consecutive positive
number

Step 2. n(n+1) be the product between these positive integers.

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

Step 4. Then using Steps 2, 3 and the problem statement yields, n*(n+1)=2n+1+29

Step 5. The following steps will solve the equation in Step 4.

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


YOUR ANSWER


  • This is an equation! Solutions: n=6,n=-5.
  • Graphical form: Equation n%2A%28n%2B1%29=2n%2B1%2B29 was fully solved.
  • Text form: n*(n+1)=2n+1+29 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2A%28n%2B1%29=2n%2B1%2B29+%29
    For tutors: simplify_cartoon( n*(n+1)=2n+1+29 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2A%28n%2B1%29=2%2An%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+29+%29.
Added fractions or integers together
It becomes n%2A%28n%2B1%29=2%2An%2Bhighlight_green%28+30+%29.
Look at n%2A%28n%2B1%29=highlight_red%28+2%2An%2B30+%29.
Moved these terms to the left highlight_green%28+-2%2An+%29,highlight_green%28+-30+%29
It becomes n%2A%28n%2B1%29-highlight_green%28+2%2An+%29-highlight_green%28+30+%29=0.
Look at highlight_red%28+n%2A%28n%2B1%29+%29-2%2An-30=0.
Expanded term n by using associative property on %28n%2B1%29
It becomes highlight_green%28+n%2An+%29%2Bhighlight_green%28+n%2A1+%29-2%2An-30=0.
Look at n%2An%2Bn%2Ahighlight_red%28+1+%29-2%2An-30=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes n%2An%2Bn-2%2An-30=0.
Look at highlight_red%28+n+%29%2Ahighlight_red%28+n+%29%2Bn-2%2An-30=0.
Reduce similar several occurrences of highlight_red%28+n+%29 to highlight_green%28+n%5E2+%29
It becomes highlight_green%28+n%5E2+%29%2Bn-2%2An-30=0.
Look at n%5E2%2Bhighlight_red%28+n+%29-highlight_red%28+2%2An+%29-30=0.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+-2%2An+%29 replacing them with highlight_green%28+%281-2%29%2An+%29
It becomes n%5E2%2Bhighlight_green%28+%281-2%29%2An+%29-30=0.
Look at n%5E2%2B%28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2An-30=0.
Added fractions or integers together
It becomes n%5E2%2B%28highlight_green%28+-1+%29%29%2An-30=0.
Look at n%5E2%2B%28highlight_red%28+-1+%29%29%2An-30=0.
Removed extra sign in front of -1
It becomes n%5E2%2B%28-highlight_green%28+1+%29%29%2An-30=0.
Look at n%5E2%2Bhighlight_red%28+%28-highlight_red%28+1+%29%29%2An+%29-30=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes n%5E2-highlight_green%28+1+%29%2An-30=0.
Look at n%5E2-highlight_red%28+1+%29%2An-30=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes n%5E2-n-30=0.
Look at highlight_red%28+n%5E2-n-30+%29=0.
Equation highlight_red%28+n%5E2-n-30=0+%29 is a quadratic equation: n^2-n-30 =0, and has solutions 6,-5
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=6,n=-5.

Universal Simplifier and Solver


Done!



Step 6. Select the positive solution and in this case it's n=6.

Step 7. So the integers are 6 and 7. Note: The product is 42 which is 29 more than their sum of 13.

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