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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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

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)
if the numerator is increased by eight and denominator is doubled we get 2/5 translates to
(ii)
cross multiply in both (i) and (ii) to get
(iii)
(iv)
pull the a and b parts to one side as
(v)
(vi)
multiply (v) by 2 and (vi) by -9 to get
(vii)
(viii)
add down to get
(ix)
So, a = 12
Sub this into (iv) we get
(x)
solving for b, we get
b = 25.
So our original fraction is