SOLUTION: A number, half of that number, and one third of that number are added. the result is 22. What is the original number?

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Question 775422: A number, half of that number, and one third of that number are added. the result is 22. What is the original number?

Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
let the number be x, then
x+x/2+x/3=22 solve for x, common denominator would be 6, so
6x%2F6%2B3x%2F6%2B2x%2F6=22 now that all the x terms have common denominator we can combine them...add the tops, leave the bottom
%286x%2B3x%2B2x%29%2F6=22
11x%2F6=22 now multiply each side by the reverse of what's in front of x, so by 6/11, this will give you x by itself
x=22%2A%286%2F11%29 you can reduce top and bottom by 11 (ie 22/11=2 and 11/11=1)
x=2%2A6
x=12