SOLUTION: If 3 times the smaller of two consecutive integers is added to 4 times the larger, the result is 102, Find the larger integer.

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Question 215166: If 3 times the smaller of two consecutive integers is added to 4 times the larger, the result is 102, Find the larger integer.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If 3 times the smaller of two consecutive integers is added to 4 times the larger, the result is 102, Find the larger integer.

Step 1. Let n be one integer and let n+1 be the next consecutive integer.

Step 2. Let 4(n+1) is 4 times the larger integer

Step 3. Let 3n is 3 times the smaller integer

Step 4. 3n+4(n+1)=102 3 times the smaller of two consecutive integers is added to 4 times the larger, the result is 102

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=14.
  • Graphical form: Equation 3n%2B4%2A%28n%2B1%29=102 was fully solved.
  • Text form: 3n+4*(n+1)=102 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3n%2B4%2A%28n%2B1%29=102+%29
    For tutors: simplify_cartoon( 3n+4*(n+1)=102 )
  • 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+102+%29.
Moved these terms to the left highlight_green%28+-102+%29
It becomes 3%2An%2B4%2A%28n%2B1%29-highlight_green%28+102+%29=0.
Look at 3%2An%2Bhighlight_red%28+4%2A%28n%2B1%29+%29-102=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+%29-102=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+1+%29-102=0.
Multiplied numerator integers
It becomes 3%2An%2B4%2An%2Bhighlight_green%28+4+%29-102=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+4+%29-highlight_red%28+102+%29=0.
Added fractions or integers together
It becomes 3%2An%2B4%2An%2Bhighlight_green%28+-98+%29=0.
Look at 3%2An%2B4%2An%2Bhighlight_red%28+-98+%29=0.
Removed extra sign in front of -98
It becomes 3%2An%2B4%2An-highlight_green%28+98+%29=0.
Look at highlight_red%28+3%2An+%29%2Bhighlight_red%28+4%2An+%29-98=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+%29-98=0.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+4+%29%29%2An-98=0.
Added fractions or integers together
It becomes %28highlight_green%28+7+%29%29%2An-98=0.
Look at highlight_red%28+%28highlight_red%28+7+%29%29%2An+%29-98=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes highlight_green%28+7+%29%2An-98=0.
Look at highlight_red%28+7%2An-98+%29=0.
Solved linear equation highlight_red%28+7%2An-98=0+%29 equivalent to 7*n-98 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=14.

Universal Simplifier and Solver


Done!



With n=14 , then n+1=15

Check 3*14+4*15=102 or 102=102 which is a true statement

Step 6. The integers are 14 and 15 where 15 is the larger integer.

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.

And good luck in your studies!

Respectfully,
Dr J