Question 30672
First, write an equation to represent the problem:

Let x = the number you're looking for.

"one half of a number..." = {{{x/2}}}

"...3 more than one-sixth the same number" = {{{(x/6)+3}}}

The equation now is: {{{(x/2)=(x/6)+3}}}

Now, solve for x:

{{{(x/2)-(x/6)=3}}}  [subtract both sides by (x/6)]


{{{6*((x/2)-(x/6))=6*3}}} [multiply both sides by 6 to get rid of the fraction]


{{{3x-x=18}}}  [simplify both sides: distribute the 6 on the left-hand side]


{{{2x=18}}}  [simplify the left side]


{{{x=9}}}  [divide both sides by 2]


You can double check whether your answer is right by applying the given conditions to the answer:

"one half of a number":  9/2 = 4.5

"is 3 more than one-sixth the same number": 9/6 = 1.5... 3 more -> 4.5