A box contains some red marbles and white marbles.  The ratio of red to white marbles in this box is $3:2$.  Pip puts some red balls into the box, and the ratio of red to white balls becomes $5:3$.  Then Bud puts some white balls into the box, and the ratio of red to white balls becomes $5:4$.  Given that the number of balls put by Bud is $100$ more than the number of balls put by Pip.  How many white balls are there in the box at first? 
Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions