4. Pizza and Pop
Two friends went out for pizza and pop after work one day. They each ordered and drank
one large pop and ate part of their pizza. They then decided they were still thirsty, so Mary
went up to get another pop. Jordan didn't have any money, so she asked if she could share
some of Mary's pop. Mary then poured half of her pop into Jordan's glass. Jordan
protested, saying it was too much, and she poured one-third of the pop in her glass back
into Mary's glass. Mary insisted that Jordan have some more, so she poured one-fourth of
the pop in her glass back into Jordan's glass. Of course, Jordan would not take so much
pop, so she poured one-fifth of the pop in her glass back into Mary's glass. This went on for
quite a while, with each pouring increasing the denominator of the fraction by 1. After 99
pourings, they decided to stop. At this point, how full was each glass of pop?