SOLUTION: a fraction is such that if the numerator is multiplied by three and the denominator reduced by three we get 18/11, but if the numerator is increased by eight and denominator is dou

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Question 257462: a fraction is such that if the numerator is multiplied by three and the denominator reduced by three we get 18/11, but if the numerator is increased by eight and denominator is doubled we get 2/5. find the fraction.
Found 2 solutions by richwmiller, drk:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
let fraction =a/b
3a/(b-3)=18/11
(a+8)/2b=2/5
a=12 b=25
check
3*12/22=36/22=18/11
ok
check
12+8/50=2/5
20/50=2/5
2/5=2/5
ok

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
First let the fraction be a/b, where b not = 0.
We start with the first bit of information:
If the numerator is multiplied by three and the denominator reduced by three we get 18/11 translates to
(i) 3a%2F%28b-3%29+=+18%2F11
if the numerator is increased by eight and denominator is doubled we get 2/5 translates to
(ii) %28a%2B8%29%2F2b+=+2%2F5
cross multiply in both (i) and (ii) to get
(iii) 33a+=+18b+-+54
(iv) 5a+%2B+40+=+4b
pull the a and b parts to one side as
(v) 33a+-+18b+=+-54
(vi) 5a+-+4b+=+-40
multiply (v) by 2 and (vi) by -9 to get
(vii) 66a+-+36b+=+-108
(viii) -45a+%2B+36b+=+360
add down to get
(ix) 21a+=+252
So, a = 12
Sub this into (iv) we get
(x) 5%2A12+%2B+40+=+4b
solving for b, we get
b = 25.
So our original fraction is
a%2Fb+=+12%2F25