SOLUTION: what is 3 times the smaller of two consecutive odd intergers is equal to twice the greater intergers plus thirteen

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Question 216572: what is 3 times the smaller of two consecutive odd intergers is equal to twice the greater intergers plus thirteen
Found 2 solutions by drj, solver91311:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
What is 3 times the smaller of two consecutive odd integers is equal to twice the greater integers plus thirteen.

Step 1. Let n be the smaller integer and n+2 be the larger and consecutive odd integer

Step 2. Let 3n be three times the smaller of two consecutive odd integers.

Step 3. Let 2(n+2) be twice the larger integers.

Step 4. Then, 3n=2(n+2)+13 since 3 times the smaller of two consecutive odd integers is equal to twice the greater integers plus thirteen.

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=17.
  • Graphical form: Equation 3n=2%2A%28n%2B2%29%2B13 was fully solved.
  • Text form: 3n=2*(n+2)+13 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3n=2%2A%28n%2B2%29%2B13+%29
    For tutors: simplify_cartoon( 3n=2*(n+2)+13 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2An=highlight_red%28+2%2A%28n%2B2%29%2B13+%29.
Moved these terms to the left highlight_green%28+-2%2A%28n%2B2%29+%29,highlight_green%28+-13+%29
It becomes 3%2An-highlight_green%28+2%2A%28n%2B2%29+%29-highlight_green%28+13+%29=0.
Look at 3%2An-highlight_red%28+2%2A%28n%2B2%29+%29-13=0.
Expanded term -2 by using associative property on %28n%2B2%29
It becomes 3%2An-highlight_green%28+2%2An+%29-highlight_green%28+2%2A2+%29-13=0.
Look at 3%2An-2%2An-highlight_red%28+2+%29%2Ahighlight_red%28+2+%29-13=0.
Multiplied numerator integers
It becomes 3%2An-2%2An-highlight_green%28+4+%29-13=0.
Look at 3%2An-2%2An-highlight_red%28+4+%29-highlight_red%28+13+%29=0.
Added fractions or integers together
It becomes 3%2An-2%2An%2Bhighlight_green%28+-17+%29=0.
Look at 3%2An-2%2An%2Bhighlight_red%28+-17+%29=0.
Removed extra sign in front of -17
It becomes 3%2An-2%2An-highlight_green%28+17+%29=0.
Look at highlight_red%28+3%2An+%29-highlight_red%28+2%2An+%29-17=0.
Eliminated similar terms highlight_red%28+3%2An+%29,highlight_red%28+-2%2An+%29 replacing them with highlight_green%28+%283-2%29%2An+%29
It becomes highlight_green%28+%283-2%29%2An+%29-17=0.
Look at highlight_red%28+%283-2%29+%29%2An-17=0.
Remove extraneous '1' from product highlight_red%28+%283-2%29+%29
It becomes n-17=0.
Look at highlight_red%28+n-17+%29=0.
Solved linear equation highlight_red%28+n-17=0+%29 equivalent to n-17 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=17.

Universal Simplifier and Solver


Done!



n=17 and n%2B2=19

Check...3n=2%28n%2B2%29%2B13 = 3%2A17=2%2A19%2B13 or 51=38%2B13=51... a true statement.

Step 5. ANSWER: The consecutive odd integers are 17 and 19.

I hope the above steps were helpful.

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http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I don't know what intergers are. But I will presume you meant integers.

Let represent the smaller of two consecutive odd integers.

If you add 1 to that, you get the next consecutive integer, but it is even. If you add 2, you get the next consecutive odd integer.

Then must represent the larger of the two integers.

3 times the smaller is

Twice the larger is

So:



Solve for to get the smaller integer. Add 2 to get the larger one.

John