SOLUTION: at a school 2/3 of the students are taking chemistry, 1/3 of the remaining students are taking physics, and the rest are taking biology. no student is taking more than one science

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: at a school 2/3 of the students are taking chemistry, 1/3 of the remaining students are taking physics, and the rest are taking biology. no student is taking more than one science       Log On


   

Question 669994: at a school 2/3 of the students are taking chemistry, 1/3 of the remaining students are taking physics, and the rest are taking biology. no student is taking more than one science class. if 66 students are taking biology, how many students are in the class?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of students in the class
given:
2/3 take chemistry, so there are 1/3 remaining
1/3 of those take physics, and that is
+%281%2F3%29%2A%281%2F3%29+=+1%2F9+ of the students
---------------------------------
So far I have +%282%2F3%29%2An+%2B+%281%2F9%29%2An+=+%287%2F9%29%2An+
That means there is +n+-+%287%2F9%29%2An+=+%282%2F9%29%2An+
students remaining.
-----------------
I am told that +%282%2F9%29%2An+=+66+
+n+=+%289%2F2%29%2A66+
+n+=+297+
There are 297 students in the class
------------------------------
check:
2/3 take chemistry
+%282%2F3%29%2A297+=+198+
There are +297+-+198+=+99+ remaining
1/3 of those take physics
+%281%2F3%29%2A99+=+33+ take physics
There are +99+-+33+=+66+ remaining
and they take biology.
OK