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
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?
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