Question 38383
I hate when that happens...but seriously folks...
Let x be the original numerator.
Let y be the original denominator.
Then we can say that
x/y = 2/3
Now look at the second set of facts...
(x + 10) / (y + 20) = 3/5
If we cross-multiply both equations we can solve them...like this...
2y = 3x
5(x + 10) = 3(y + 20)
Now
y = 3/2 x and we can substitute that into the second equation...
5(x + 10) = 3(3/2 x + 20)
5x + 50 = 9/2 x + 60
Now subtract 9/2 x from both sides and then subtract 50 from both sides...
1/2 x + 50 = 60
1/2 x = 10 and thus
x = 20
Looking at the very first equation, if x = 20,
y = 30 and the original fraction is
20/30