SOLUTION: this question is so easy but yet i just can't figure it out. It's driving me crazy. I just need the fomula, i think. okay so here it is. One-third of a number is 5 less than half

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Question 134143: this question is so easy but yet i just can't figure it out. It's driving me crazy. I just need the fomula, i think. okay so here it is.
One-third of a number is 5 less than half of the same number. What is the number?
Found 3 solutions by josmiceli, Earlsdon, nycsharkman:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First say the number = n, then just carefully read the question
One-third of the number would be n%2F3
5 less than 1/2 of the number would be n%2F2+-+5
The problem says:
n%2F3+=+n%2F2+-+5
multiply both sides by 6
2n+=+3n+-+30
n+=+30
check:
n%2F3+=+n%2F2+-+5
30%2F3+=+30%2F2+-+5
10+=+15+-+5
10+=+10
OK

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be n:
%28n%2F3%29+=+%28n%2F2%29-5 Simplify and solve for n. Multiply both sides by 3.
n+=+%283n%2F2%29-15 Now multiply both sides by 2.
2n+=+3n-30 Add 30 to both sides.
2n%2B30+=+3n Finally, subtract 2n from both sides.
30+=+n
The number is 30.
Check:
30%2F3+=+%2830%2F2%29+-+5
10+=+15-5
10+=+10

Answer by nycsharkman(136) About Me  (Show Source):
You can put this solution on YOUR website!
One-third of a number is 5 less than half of the same number. What is the number?
Let x = the missing number
1/3(x) = (1/2)(x) - 5
We now solve for x.
(1/3)(x) can be written as simply x/3.
(1/2)(x) can be written as simply x/2.
We now have a fractional equation:
x/3 = x/2 - 5....Much easier to work with, right?
To remove the fractions, we multiply both sides of the equation by the LCD, which is 6.
x/3 times 6 = 2x
x/2 times 6 = 3x
-5 times 6 = -30
We now have a linear equation:
2x = 3x - 30
Subtract 3x from 2x.
2x - 3x = -30
-x = -30
Divide both sides by -1 to find our missing number.
x = -30/-1
x = 30
So, what is the missing number? The missing number is 30.