Three students and a sliced pizza

Puzzle: Three students, Emma, Peter, and James, shared a pizza. Emma ate a quarter, Peter ate a third, which resulted in Peter having 2 slices more than Emma. How many slices did James have?

Answer: James had 10 slices  

Solution: Emma and Peter's shares are given as fractions (1/4 and 1/3). This allows us to calculate James's share because the sum of all shares must amount to one pizza, Fig. 2, left.

1/4 + 1/3 = 3/12 + 4/12 = 7/12 (Peter and Emma's shares combined)

12/12 - 7/12 = 5/12 (James's share)

The difference between Emma's and Peter's shares is given as 2 slices. This information helps us determine the number of slices in a single fraction (Fig. 2, right). The difference in shares between Peter and Emma is:

 4/12 - 3/12 = 1/12 

By converting James's share (5/12) into slices at a rate of 2 slices for each 1/12 of the pizza, we get:

The pizza was cut into 24 slices. To determine each student's share, we split it into 12 parts, each containing 2 slices. Emma consumed 3 parts, 3 parts x 2 slices = 6 slices. Peter consumed 4 parts, 4 parts x 2 slices = 8 slices, having 2 slices more, 8 - 6 = 2. James ate 5 parts, 5 parts x 2 slices = 10 slices.