SOLUTION: if five times the smaller of two consecutive integers is added to three times the, the result is 59. Find bothe numbers

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Question 223809: if five times the smaller of two consecutive integers is added to three times the, the result is 59. Find bothe numbers
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If five times the smaller of two consecutive integers is added to three times the larger integer, the result is 59. Find both numbers.

Step 1. Let n be one integer.

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

Step 3. Let 5n be five times the smaller integer.

Step 4. Let 3(n+1) be three times the larger integer.

Step 5. Then 5n+3(n+1)=59 since five times the smaller of two consecutive integers is added to three times the larger integer, the result is 59.

Step 6. Solving the equation in Step 5 leads to the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: n=7.
  • Graphical form: Equation 5n%2B3%2A%28n%2B1%29=59 was fully solved.
  • Text form: 5n+3*(n+1)=59 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5n%2B3%2A%28n%2B1%29=59+%29
    For tutors: simplify_cartoon( 5n+3*(n+1)=59 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2An%2B3%2A%28n%2B1%29=highlight_red%28+59+%29.
Moved these terms to the left highlight_green%28+-59+%29
It becomes 5%2An%2B3%2A%28n%2B1%29-highlight_green%28+59+%29=0.
Look at 5%2An%2Bhighlight_red%28+3%2A%28n%2B1%29+%29-59=0.
Expanded term 3 by using associative property on %28n%2B1%29
It becomes 5%2An%2Bhighlight_green%28+3%2An+%29%2Bhighlight_green%28+3%2A1+%29-59=0.
Look at 5%2An%2B3%2An%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-59=0.
Multiplied numerator integers
It becomes 5%2An%2B3%2An%2Bhighlight_green%28+3+%29-59=0.
Look at 5%2An%2B3%2An%2Bhighlight_red%28+3+%29-highlight_red%28+59+%29=0.
Added fractions or integers together
It becomes 5%2An%2B3%2An%2Bhighlight_green%28+-56+%29=0.
Look at 5%2An%2B3%2An%2Bhighlight_red%28+-56+%29=0.
Removed extra sign in front of -56
It becomes 5%2An%2B3%2An-highlight_green%28+56+%29=0.
Look at highlight_red%28+5%2An+%29%2Bhighlight_red%28+3%2An+%29-56=0.
Eliminated similar terms highlight_red%28+5%2An+%29,highlight_red%28+3%2An+%29 replacing them with highlight_green%28+%285%2B3%29%2An+%29
It becomes highlight_green%28+%285%2B3%29%2An+%29-56=0.
Look at %28highlight_red%28+5+%29%2Bhighlight_red%28+3+%29%29%2An-56=0.
Added fractions or integers together
It becomes %28highlight_green%28+8+%29%29%2An-56=0.
Look at highlight_red%28+%28highlight_red%28+8+%29%29%2An+%29-56=0.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes highlight_green%28+8+%29%2An-56=0.
Look at highlight_red%28+8%2An-56+%29=0.
Solved linear equation highlight_red%28+8%2An-56=0+%29 equivalent to 8*n-56 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=7.

Universal Simplifier and Solver


Done!



With n=7, then n+1=8. Check sum... 5*7+3*8=35+24=59 which is a true statement.

Step 7. The consecutive integers are 7 and 8.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J