4/7 of the students in a school play tennis and 60% of the students play basketball. The rest of the students play both tennis and basketball. If 120 students joined both tennis and basketball, how many students are there in the school?
Restating your problem:
let the total number of students be x
number playing tennis = 4x/7
number playing bball = 3x/5 <------ 66% = 3/5
4x/7 + 3x/5 - 120 = x
times 35 , the LCD
20x + 21x - 4200 = 35x
6x = 4200
x = 700 <----- total in school, assuming all play at least one of the two sports
check:
4/7 of 700 = 400 <--- play tennis
3/5 of 700 = 420 <---- play bball
120 play both
400+420-120 = 700
Make a Venn diagram , enter the values to verify