how many students are there

Question

a group of students played two types of board games during recess. 1/3 of them played chess and 3/5 of them played scrabble. 1/8 of the students played both games and 23 students did not play games at all. how many students were there?

Answer 1

Given:

1/3 of the students played chess

3/5 of the students played scrabble

1/8 of the students played both games

23 students did not play games at all

 

We need to figure out what part of the students didn't play games at all. However, if we just add the 1/3 and 3/5, this is too big because some students played both games.

 

We need to:

 

1/3 + 3/5 - 1/8 = part of students playing any game

 

5/15 + 9/15 - 1/8

14/15 - 1/8

112/120 - 15/120

97/120

 

If 97 out of 120 students are playing, How do we figure out how many students are not?

 

We subtract:

 

120 - 97 = 23

 

23/120 students are not playing. Now, we need to compare this to the original question where we know that 23 students are not playing and we can see that there are 120 students total.