Mary ale 4 1/2 pears and Carmie ate 7 2/4 pears. If they finished all the pears in a box, how many pears were in the box?
To add the number of pears Mary and Carmie ate, convert the mixed numbers to improper fractions: 4 1/2 is 9/2 and 7 2/4 is 18/4.
Then add the fractions: 9/2 + 18/4 = 36/8 + 18/8 = <<36/8+18/8=54/8=6 3/4>>6 3/4.
This means Mary and Carmie ate 6 3/4 pears.
Since they ate all the pears in the box, the box contained 6 3/4 pears. Answer: \boxed{6 \frac{3}{4}}.