SOLUTION: one third of the result obtained by adding 5 to a certain numnber is equal to one-half of the result obtained when 5 is subtracted from the number. Find the number

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Question 714706: one third of the result obtained by adding 5 to a certain numnber is equal to one-half of the result obtained when 5 is subtracted from the number. Find the number
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
a certain number = x
add 5 to a certain number = (x+5)
one third of (add 5 to a certain number) = (1/3)(x+5)
5 subtracted from a the certain number = (x-5)
one half of (5 subtracted from a the certain number) = (1/2)(x-5)

So "one third of the result obtained by adding 5 to a certain numnber is equal to one-half of the result obtained when 5 is subtracted from the number" translates into:
%281%2F3%29%28x%2B5%29+=+%281%2F2%29%28x-5%29

Now we solve for x. We could start by multiplying out each side but that will involve a lot of fractions. Instead we'll eliminate the the fractions by multiplying both sides of the equation by the lowest common denominator (LCD) of the two denominators. The LCD of 3 and 2 is 6.
6%28%281%2F3%29%28x%2B5%29%29+=+6%28%281%2F2%29%28x-5%29%29
which simplifies as follows:
2%28x%2B5%29+=+3%28x-5%29
2x%2B10+=+3x-15
With the fractions gone the rest is easy. Subtractin 2x from each side:
10+=+x+-+15
Adding 15 to each side:
25+=+x