SOLUTION: If three times the smaller of two consecutive integers is added to four times the larger, the result is 39. Find the smaller integer.

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Question 224200: If three times the smaller of two consecutive integers is added to four times the larger, the result is 39. Find the smaller integer.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If three times the smaller of two consecutive integers is added to four times the larger, the result is 39. Find the smaller integer.

Step 1. Let n be the smaller integer.

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

Step 3. Let 3n be three times the smaller integer.

Step 4. Let 4(n+1) be four times the larger integer.

Step 5. Then 3n+4(n+1)=39 since three times the smaller of two consecutive integers is added to four times the larger will result in 39.

Step 6. Solving the equation in Step yields the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: n=5.
  • Graphical form: Equation 3n%2B4%2A%28n%2B1%29=39 was fully solved.
  • Text form: 3n+4*(n+1)=39 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3n%2B4%2A%28n%2B1%29=39+%29
    For tutors: simplify_cartoon( 3n+4*(n+1)=39 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2An%2B4%2A%28n%2B1%29=highlight_red%28+39+%29.
Moved these terms to the left highlight_green%28+-39+%29
It becomes 3%2An%2B4%2A%28n%2B1%29-highlight_green%28+39+%29=0.
Look at 3%2An%2Bhighlight_red%28+4%2A%28n%2B1%29+%29-39=0.
Expanded term 4 by using associative property on %28n%2B1%29
It becomes 3%2An%2Bhighlight_green%28+4%2An+%29%2Bhighlight_green%28+4%2A1+%29-39=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+1+%29-39=0.
Multiplied numerator integers
It becomes 3%2An%2B4%2An%2Bhighlight_green%28+4+%29-39=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+4+%29-highlight_red%28+39+%29=0.
Added fractions or integers together
It becomes 3%2An%2B4%2An%2Bhighlight_green%28+-35+%29=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+-35+%29=0.
Removed extra sign in front of -35
It becomes 3%2An%2B4%2An-highlight_green%28+35+%29=0.
Look at highlight_red%28+3%2An+%29%2Bhighlight_red%28+4%2An+%29-35=0.
Eliminated similar terms highlight_red%28+3%2An+%29,highlight_red%28+4%2An+%29 replacing them with highlight_green%28+%283%2B4%29%2An+%29
It becomes highlight_green%28+%283%2B4%29%2An+%29-35=0.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+4+%29%29%2An-35=0.
Added fractions or integers together
It becomes %28highlight_green%28+7+%29%29%2An-35=0.
Look at highlight_red%28+%28highlight_red%28+7+%29%29%2An+%29-35=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes highlight_green%28+7+%29%2An-35=0.
Look at highlight_red%28+7%2An-35+%29=0.
Solved linear equation highlight_red%28+7%2An-35=0+%29 equivalent to 7*n-35 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=5.

Universal Simplifier and Solver


Done!



With n=5, then n+1=6 and check the sum 3*5+4*6=15+24=39...which is a true statement.

Step 7. ANSWER: The integers are 5 and 6

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

drjctu@gmail.com

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