Question

In a class of 33 students, 12 are girls, 10 play soccer, and 10 play chess. Moreover, it is known that 6 of the soccer players are girls, that 2 of the chess players also play soccer, and that there is exactly one girl who plays both chess and soccer. Finally, 4 girls play neither soccer nor chess. Can you figure out how many boys play soccer, chess, neither, both?

Answer 1

i had this same problem

Explanation:

Answer 2

• 4 boys play soccer
• 7 boys play chess
• 11 boys play neither
• 1 boy plays both

Explanation:

A grid can be created that shows all the possibilities. The given numbers can be filled in, and the remaining numbers computed. In the attached grid, we had to compute that 5 girls play soccer only, given that 6 play soccer and 1 plays both chess and soccer. Likewise the totals for soccer only and chess only are computed from 10 students playing each and 2 playing both.

The totals are the simple sums of row or column The red numbers are computed so as to make the totals add up correctly. The black numbers are the ones given in the problem statement (with the exception for 5 noted above).