SOLUTION: If 4 is subtracted from a certain number and the difference is divided by 4, the result is 1 more than 1/6 of the original number. Find the original number.

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Question 1157827: If 4 is subtracted from a certain number and the difference is divided by 4, the result is 1 more than 1/6 of the original number. Find the original number.
Found 2 solutions by Shin123, MathTherapy:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
The equation we get is %28x-4%29%2F4=%281%2F6%29x%2B1.
Solved by pluggable solver: Solve an equation
This is a solution to the equation:
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=24.
  • Graphical form: Equation %28x-4%29%2F4=%281%2F6%29%2Ax%2B1 was fully solved.
  • Text form: (x-4)/4=(1/6)*x+1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28x-4%29%2F4=%281%2F6%29%2Ax%2B1+%29
    For tutors: simplify_cartoon( (x-4)/4=(1/6)*x+1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %28x-4%29%2F4=highlight_red%28+%28highlight_red%28+1%2F6+%29%29%2Ax+%29%2B1.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F6+%29
It becomes %28x-4%29%2F4=highlight_green%28+1+%29%2Fhighlight_green%28+6+%29%2Ax%2B1.
Look at %28x-4%29%2F4=highlight_red%28+1+%29%2F6%2Ax%2B1.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %28x-4%29%2F4=x%2F6%2B1.
Look at %28x-4%29%2F4=highlight_red%28+x%2F6%2B1+%29.
Moved these terms to the left highlight_green%28+-x%2F6+%29,highlight_green%28+-1+%29
It becomes %28x-4%29%2F4-highlight_green%28+x%2F6+%29-highlight_green%28+1+%29=0.
Look at highlight_red%28+%28x-4%29%2F4+%29-x%2F6-1=0.
Expanded term 1%2F4 by using associative property on %28x-4%29
It becomes highlight_green%28+1%2F4%2Ax+%29-highlight_green%28+1%2F4%2A4+%29-x%2F6-1=0.
Look at highlight_red%28+1+%29%2F4%2Ax-1%2F4%2A4-x%2F6-1=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F4-1%2F4%2A4-x%2F6-1=0.
Look at x%2F4-1%2Fhighlight_red%28+4+%29%2Ahighlight_red%28+4+%29-x%2F6-1=0.
Factors 4 and 4 have greatest common factor (GCF) of 4. Reducing fraction.
It becomes x%2F4-1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+1+%29-x%2F6-1=0.
Look at x%2F4-highlight_red%28+1+%29%2F1%2Ahighlight_red%28+1+%29-x%2F6-1=0.
Multiplied numerator integers
It becomes x%2F4-highlight_green%28+1+%29%2F1-x%2F6-1=0.
Look at x%2F4-highlight_red%28+1%2F1+%29-x%2F6-highlight_red%28+1+%29=0.
Added fractions or integers together
It becomes x%2F4%2Bhighlight_green%28+-2+%29-x%2F6=0.
Look at x%2F4%2Bhighlight_red%28+-2+%29-x%2F6=0.
Moved -2 to the right of expression
It becomes x%2F4-x%2F6%2Bhighlight_green%28+-2+%29=0.
Look at x%2F4-x%2F6%2Bhighlight_red%28+-2+%29=0.
Removed extra sign in front of -2
It becomes x%2F4-x%2F6-highlight_green%28+2+%29=0.
Look at highlight_red%28+x%2F4+%29-highlight_red%28+x%2F6+%29-2=0.
Eliminated similar terms highlight_red%28+x%2F4+%29,highlight_red%28+-x%2F6+%29 replacing them with highlight_green%28+%281%2F4-1%2F6%29%2Ax+%29
It becomes highlight_green%28+%281%2F4-1%2F6%29%2Ax+%29-2=0.
Look at %28highlight_red%28+1%2F4+%29-highlight_red%28+1%2F6+%29%29%2Ax-2=0.
Added fractions or integers together
It becomes %28highlight_green%28+1%2F12+%29%29%2Ax-2=0.
Look at highlight_red%28+%28highlight_red%28+1%2F12+%29%29%2Ax+%29-2=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F12+%29
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+12+%29%2Ax-2=0.
Look at highlight_red%28+1+%29%2F12%2Ax-2=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F12-2=0.
Look at highlight_red%28+x%2F12-2+%29=0.
Solved linear equation highlight_red%28+x%2F12-2=0+%29 equivalent to 0.0833333333333333*x-2 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=24.

Universal Simplifier and Solver


Done!
0=0;x=24
x%2F12-2=0 x%2F12=2 highlight%28x=24%29. Click here to use the solver above.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

If 4 is subtracted from a certain number and the difference is divided by 4, the result is 1 more than 1/6 of the original number. Find the original number.
Let number be N

Then we get: 

3(N - 4) = 2N + 12 ------ Multiplying by LCD, 12

3N - 12 = 2N + 12

3N - 2N = 24

Number, or highlight_green%28matrix%281%2C3%2C+N%2C+%22=%22%2C+24%29%29