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 gam

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

 

(1/3 + 3/5 - 1/8)X + 23 = X

 

(40/120 + 72/120 - 15/120)X = X-23

 

 (97/120)X = X - 23

 

 0 = 23/120X - 23

 

23 = 23/120 X

 

X = 120

 

120 students

 

1/3 played chess , with some scrabble : 1/3 x 120 = 40

 

3/5 played scrabble with some chess: 3/5 x 120 = 72

 

1/8 played both: 1/8 x 120 = 15

 

40 + 72 - 15 + 23 = 112 - 15 + 23 = 97+23 = 120