SOLUTION: find two consecutive odd integers such that their product is 15 more than 3 times their sum

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Question 214176This question is from textbook
: find two consecutive odd integers such that their product is 15 more than 3 times their sum This question is from textbook

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find two consecutive odd integers such that their product is 15 more than 3 times their sum.

Step 1. Let n be an odd integer then n+2 be the next odd consecutive integer

Step 2. n(n+2) is the product of the two odd integers.

Step 3. n+n+2 is the sum of the two odd integers.

Step 4. n(n+2)=15+3(n+n+2) product is 15 more than sum.

Step 5. Solve the equation in Step 4 using the following steps.

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


YOUR ANSWER


  • This is an equation! Solutions: n=7,n=-3.
  • Graphical form: Equation n%2A%28n%2B2%29=15%2B3%2A%28n%2Bn%2B2%29 was fully solved.
  • Text form: n*(n+2)=15+3*(n+n+2) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2A%28n%2B2%29=15%2B3%2A%28n%2Bn%2B2%29+%29
    For tutors: simplify_cartoon( n*(n+2)=15+3*(n+n+2) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2A%28n%2B2%29=highlight_red%28+15+%29%2B3%2A%28n%2Bn%2B2%29.
Moved 15 to the right of expression
It becomes n%2A%28n%2B2%29=3%2A%28n%2Bn%2B2%29%2Bhighlight_green%28+15+%29.
Look at n%2A%28n%2B2%29=3%2A%28highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B2%29%2B15.
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 n%2A%28n%2B2%29=3%2A%28highlight_green%28+%281%2B1%29%2An+%29%2B2%29%2B15.
Look at n%2A%28n%2B2%29=3%2A%28%28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B2%29%2B15.
Added fractions or integers together
It becomes n%2A%28n%2B2%29=3%2A%28%28highlight_green%28+2+%29%29%2An%2B2%29%2B15.
Look at n%2A%28n%2B2%29=3%2A%28highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B2%29%2B15.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes n%2A%28n%2B2%29=3%2A%28highlight_green%28+2+%29%2An%2B2%29%2B15.
Look at n%2A%28n%2B2%29=highlight_red%28+3%2A%282%2An%2B2%29%2B15+%29.
Moved these terms to the left highlight_green%28+-3%2A%282%2An%2B2%29+%29,highlight_green%28+-15+%29
It becomes n%2A%28n%2B2%29-highlight_green%28+3%2A%282%2An%2B2%29+%29-highlight_green%28+15+%29=0.
Look at highlight_red%28+n%2A%28n%2B2%29+%29-3%2A%282%2An%2B2%29-15=0.
Expanded term n by using associative property on %28n%2B2%29
It becomes highlight_green%28+n%2An+%29%2Bhighlight_green%28+n%2A2+%29-3%2A%282%2An%2B2%29-15=0.
Look at highlight_red%28+n+%29%2Ahighlight_red%28+n+%29%2Bn%2A2-3%2A%282%2An%2B2%29-15=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%2A2-3%2A%282%2An%2B2%29-15=0.
Look at n%5E2%2Bn%2A2-highlight_red%28+3%2A%282%2An%2B2%29+%29-15=0.
Expanded term -3 by using associative property on %282%2An%2B2%29
It becomes n%5E2%2Bn%2A2-highlight_green%28+3%2A2%2An+%29-highlight_green%28+3%2A2+%29-15=0.
Look at n%5E2%2Bn%2A2-highlight_red%28+3+%29%2Ahighlight_red%28+2+%29%2An-3%2A2-15=0.
Multiplied numerator integers
It becomes n%5E2%2Bn%2A2-highlight_green%28+6+%29%2An-3%2A2-15=0.
Look at n%5E2%2Bn%2A2-6%2An-highlight_red%28+3+%29%2Ahighlight_red%28+2+%29-15=0.
Multiplied numerator integers
It becomes n%5E2%2Bn%2A2-6%2An-highlight_green%28+6+%29-15=0.
Look at n%5E2%2Bn%2A2-6%2An-highlight_red%28+6+%29-highlight_red%28+15+%29=0.
Added fractions or integers together
It becomes n%5E2%2Bn%2A2-6%2An%2Bhighlight_green%28+-21+%29=0.
Look at n%5E2%2Bn%2A2-6%2An%2Bhighlight_red%28+-21+%29=0.
Removed extra sign in front of -21
It becomes n%5E2%2Bn%2A2-6%2An-highlight_green%28+21+%29=0.
Look at n%5E2%2Bhighlight_red%28+n%2A2+%29-highlight_red%28+6%2An+%29-21=0.
Eliminated similar terms highlight_red%28+n%2A2+%29,highlight_red%28+-6%2An+%29 replacing them with highlight_green%28+%282-6%29%2An+%29
It becomes n%5E2%2Bhighlight_green%28+%282-6%29%2An+%29-21=0.
Look at n%5E2%2B%28highlight_red%28+2+%29-highlight_red%28+6+%29%29%2An-21=0.
Added fractions or integers together
It becomes n%5E2%2B%28highlight_green%28+-4+%29%29%2An-21=0.
Look at n%5E2%2B%28highlight_red%28+-4+%29%29%2An-21=0.
Removed extra sign in front of -4
It becomes n%5E2%2B%28-highlight_green%28+4+%29%29%2An-21=0.
Look at n%5E2%2Bhighlight_red%28+%28-highlight_red%28+4+%29%29%2An+%29-21=0.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes n%5E2-highlight_green%28+4+%29%2An-21=0.
Look at highlight_red%28+n%5E2-4%2An-21+%29=0.
Equation highlight_red%28+n%5E2-4%2An-21=0+%29 is a quadratic equation: n^2-4*n-21 =0, and has solutions 7,-3
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=7,n=-3.

Universal Simplifier and Solver


Done!



Step 6. There are two solutions 7 and 9 is one solution set and the other -3 and -1 is another solution set.

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