SOLUTION: the difference between two numbers is 22. If the larger number is 4 more than twice the smaller. Find the numbers

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: the difference between two numbers is 22. If the larger number is 4 more than twice the smaller. Find the numbers       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 225986: the difference between two numbers is 22. If the larger number is 4 more than twice the smaller. Find the numbers
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between two numbers is 22. If the larger number is 4 more than twice the smaller. Find the numbers

Step 1. Let x be one number

Step 2. Let 22+x be the larger number and since the difference between the two numbers is 22.

Step 3. Let 2x be twice the smaller.

Step 4. 22+x=4+2x since the larger number is 4 more than twice the smaller.

Step 5. Solving the equation in Step 4 leads to the following steps.

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


YOUR ANSWER


  • This is an equation! Solutions: x=18.
  • Graphical form: Equation 22%2Bx=4%2B2x was fully solved.
  • Text form: 22+x=4+2x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+22%2Bx=4%2B2x+%29
    For tutors: simplify_cartoon( 22+x=4+2x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+22+%29%2Bx=4%2B2x.
Moved 22 to the right of expression
It becomes x%2Bhighlight_green%28+22+%29=4%2B2x.
Look at x%2B22=highlight_red%28+4+%29%2B2%2Ax.
Moved 4 to the right of expression
It becomes x%2B22=2%2Ax%2Bhighlight_green%28+4+%29.
Look at x%2B22=highlight_red%28+2%2Ax%2B4+%29.
Moved these terms to the left highlight_green%28+-2%2Ax+%29,highlight_green%28+-4+%29
It becomes x%2B22-highlight_green%28+2%2Ax+%29-highlight_green%28+4+%29=0.
Look at x%2Bhighlight_red%28+22+%29-2%2Ax-highlight_red%28+4+%29=0.
Added fractions or integers together
It becomes x%2Bhighlight_green%28+18+%29-2%2Ax=0.
Look at x%2Bhighlight_red%28+18+%29-2%2Ax=0.
Moved 18 to the right of expression
It becomes x-2%2Ax%2Bhighlight_green%28+18+%29=0.
Look at highlight_red%28+x+%29-highlight_red%28+2%2Ax+%29%2B18=0.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+-2%2Ax+%29 replacing them with highlight_green%28+%281-2%29%2Ax+%29
It becomes highlight_green%28+%281-2%29%2Ax+%29%2B18=0.
Look at %28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2Ax%2B18=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2Ax%2B18=0.
Look at %28highlight_red%28+-1+%29%29%2Ax%2B18=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2Ax%2B18=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2Ax+%29%2B18=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2Ax%2B18=0.
Look at -highlight_red%28+1+%29%2Ax%2B18=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2B18=0.
Look at highlight_red%28+-x%2B18+%29=0.
Solved linear equation highlight_red%28+-x%2B18=0+%29 equivalent to -x+18 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=18.

Universal Simplifier and Solver


Done!



With x=18, then 22+x=40

Check with equation four 22+x=4+2x or 40=4+2*18 or 40=40 which is a true statement.

Step 6. Then numbers are 18 and 40


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

http://www.FreedomUniversity.TV
http://www.Facebook.com/FreedomUniversity.TV
http://www.Twitter.com/FreedomUTV