SOLUTION: At a certain school, 240 of the students take math, 180 of the students take grammar, and 100 of the students take both. If every student must study either math or grammar, how ma

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Question 294: At a certain school, 240 of the students take math, 180 of the students take grammar, and 100 of the students take both. If every student must study either math or grammar, how many students attend this school?
Answer by AnlytcPhil(1116) About Me  (Show Source):
You can put this solution on YOUR website!

At a certain school, 240 of the students take math, 180 of the students take
grammar, and 100 of the students take both. If every student must study either
math or grammar, how many students attend this school?<<

Let x = number who take math ONLY
Let y = number who take grammar ONLY
>>...100 of the students take both...<<
>>...240 of the students take math...<<
Translation: The number who take math ONLY + the number who take BOTH = 240
       x + 100 = 240
             x = 240 - 100
             x = 140 
>>...180 of the students take grammar...<<
The number who take grammar ONLY + the number who take BOTH = 180
       y + 100 = 180
             y = 180 - 100
             y = 80
>>...If every student must study either math or grammar, how many students
attend this school?...<<


Number who attend school =

   number who take math ONLY + 

      number who take grammar ONLY +

         number who take BOTH =

            140 + 80 + 100 = 320 attend the school.

Edwin