SOLUTION: The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then th

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Question 972769:
The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1
3
of it. Find the original fraction.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
original fraction is (x-5) / x

when you multiply the numerator by 2 and add 16 to the denominator, the original fraction is reduced by 1/3.

this means the original fraction is equal to 2/3 times what it was originally.

your equation is:

(x-5) * 2 divided by x + 16
is equal to 2/3 * (x-5) / x

this is equivalent to:

(x-5) * 2 / (x + 16) = ((x-5) * 2) / 3x

multiply both sides of the equation by (x+16) and by (3x) and you get:

(x-5) * 2 * (3x) = (x-5) * 2 * (x+16)

divide both sides of this equation by (x-5) and you get:

2 * 3x = 2 * (x + 16)

simplify to get:

6x = 2x + 32

subtract 2x from both sides of this equation to get:

4x = 32

divide both sides of this equation by 4 to get:

x = 8

that's your solution.

your original fraction is (8-5)/8 = 3/8

your final fraction is (3 * 2) / (8 + 16) = 6 / 24 = 1/4

your original fraction of 3/8 * 2/3 = 6/24 = 1/4.

this is the same as your original fraction being reduced by 1/3.

3/8 - 1/3 * 3/8 = 3/8 - 3/24 = 9/24 - 3/24 = 6/24 = 1/4.

the questions was what is the original fraction.

the answer is that the original fraction is 3/8.