Expert: Scott A Wilson - 11/8/2009

Question
1.find a fraction which reduces to 2/3 when 3 is added to both its numerator and denominator, and reduces to 3/5 when 1 is aaded to both its numerator and denminator.
2. there ee some girls in two classrooms A and B . If 12 girls are sent from room A to room B, the number of girls in both the rooms will become equal. If 11 girls are sent from room B to room A ,then the number of girls in room A will be double te number of girls in room B. How many girls are there in each classroom?  

Answer
1.  Let the fractioin be x/y.  (x+3)/y = 2/3 and (x+1)/(y+1) = 3/5.
The first one says that 3(x+3) = 2y, of (A) y = 3(x+3)/2.
The second one says that 5(x+1) = 3(y+1), which, when multiplied, gives 3y + 3.
Since we have 5(x+1) = 3y + 3, we can see that 3y = 5(x+1) - 3.
Divide by 3 and get (B) y = (5(x+1)-3)/3.

Note that (A) and (B) both have y = ...., so set the right sides equal and solve for x.
Once this is found, solve for y.
The original fraction was x/y.

2. If 12 move over from A to B, classes are equal,
and that says the B + 12 = A - 12, so B + 24 = A.

For 11 sent from B to A, twice as many will be in A, which says 2(B-11) = A+11.

Put A = B + 24 into 2(B-11) = A+11 and solve for A.  Subtract off 24 and you have B.