Let \(x\) be the total number of students at Pascal H.S.
Let \(a\) be the total number of students who went on both the
first trip and the second trip, but did not go on the third trip.
Let \(b\) be the total number of students who went on both the
first trip and the third trip, but did not go on the second trip.
Let \(c\) be the total number of students who went on both the second trip and the third trip, but did not go on the first trip.
We note that no student went on one trip only, and that \(160\) students went on all three trips.
Since the total number of students at the school is \(x\) and each region in the diagram is labelled separately, then
\[ x = a + b + c + 160 \]
From the given information:
- \(50\%\) of the students in the school went on the first trip,
so \(0.5x = a+b+160\)
- \(80\%\) of the students in the school went on the second trip, so \(0.8x = a+c+160\)
- \(90\%\) of the students in the school went on the third trip,
so \(0.9x = b+c+160\)