SOLUTION: The sum of one-half of a number, one third of the number, and one-fourth of the same number is one-tenth. What is the number?

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Question 237623: The sum of one-half of a number, one third of the
number, and one-fourth of the same number is
one-tenth. What is the number?
Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
There might be an easier way to solve this, but I found a way to do it.
First, build the equation.
The sum of
one-half of a number... 1/2x
one third of the number... 1/3x
and one-fourth of the same number... 1/4x
is one-tenth... = 1/10
%281%2F2%29x%2B%281%2F3%29x%2B%281%2F4%29x=1%2F10
Now mulitiply entire equation by the LCD...
I multiplied 2x3x4=24, so I used 24
24%28%281%2F2%29x%2B%281%2F3%29x%2B%281%2F4%29x%29=24%2A%281%2F10%29
12x%2B8x%2B6x=%2824%2F10%29
26x=%2824%2F10%29
Now divide 26 from both sides
(this is the same as multiplying by its reciprocal... 1/26), so
x=%2824%2F10%29%2A%281%2F26%29
x=24%2F260
You may now simplify the fraction to a simpler fraction.
I'll let you work on that step, since it's the last one. :)