Question 1205027
<br>
This would be a much more interesting problem, open to a large number of different solution methods, if it asked us to find the number of stickers each of them had at the beginning.<br>
However, since the problem only asked for the total number of stickers, there seems to be one path to the solution that is by far the easiest.<br>
After Mary gave 1/3 of her stickers to Gary, the ratio of Gary to Mary was 7:5 and Gary had 32 more stickers than Mary.  Given that ratio 7:5...<br>
Let 7x = Gary's stickers
Let 5x = Mary's stickers<br>
(That is one standard way of setting up a problem when a ratio is given; whatever value x has, the ratio 7x:5x is always 7:5.)<br>
Gary had 32 more stickers than Mary:<br>
7x-5x=32
2x=32
x=16<br>
And the total numer of stickers was 7x+5x = 12x = 192.<br>
ANSWER: 192<br>