# Math

If the numerator of a fractionis multiplied by 4 and the denominatoris reduced by 2,the result is 2.if the numerator of the fraction is increase by 15 and 2 subtracted from the double of the denominator the result is 9/7, find the fraction.plz tell me step by step

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1. done. see related questions below.

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2. OK, let's see whether I can clarify it a bit.

If the original fraction is n/d, then we are told:

numerator of a fraction is multiplied by 4: change n to 4n
denominator is reduced by 2: change d to d-2

4n/(d-2) = 2

Similar changes for the 2nd half, giving us
(n+15)/(2d-2) = 9/7

Now just find n and d:

4n/(d-2) = 2
(n+15)/(2d-2) = 9/7

4n = 2(d-2)
7(n+15) = 9(2d-2)

4n = 2d-4
7n + 105 = 18d - 18

4n-2d = -4
7n-18d = -123

36n-18d = -36
7n-18d = -123

29n = 87
n=3

Now use that in 4n-2d = -4 to get
d = 8

So the original fraction is 3/8

check:

4*3/(8-2) = 12/6 = 2
(3+15)/(2*8-2) = 18/14 = 9/7

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