SOLUTION: On A half of a number is 3 more than one sixth of the same number. what is the number?

Question 119282: On A half of a number is 3 more than one sixth of the same number. what is the number?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let x represent the unknown number.
.
Then one-half of the unknown number is x divided by 2 or
.
And one-sixth of the unknown number is x divided by 6 or
.
The problem tells you that one-half x is 3 more than one-sixth x. In equation form this can
be written as:
.

.
You can get rid of the denominators by multiplying both sides of this equation (all terms) by 6
to get:
.

.
Notice on the left side the 2 in the denominator divides into the 6 in the numerator
3 times. And on the right side the 6 in the denominator divides into the 6 in the numerator
1 time. These two reductions make the equation become:
.

.
Get rid of the x on the right side by subtracting x from both sides to get:
.

.
Finally, solve for x by dividing both sides by 2 to get:
.

.
Check the answer. One half of 9 is . One sixth of 9 is . Three more than
is
.
So does equal ???
.
Yes it does because if you divide 9 by 2 the answer is 4 1/2. And if you divide 27 by 6 the
answer is 4 3/6 which is also 4 1/2.
.
So, the answer checks. The unknown number you were to find is 9.
.
Hope this helps you to understand the problem.
.
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