00:01
In this problem, we have the following situation.
00:04
We have 500 students in a science department.
00:09
And we are asking them which of the three science subjects, chemistry, mathematics and physics, they like to study.
00:17
So we have mathematics, physics and chemistry.
00:22
So let us draw some venn diagrams here.
00:28
In fact, let's put them over here because we are going to use the right -hand side for the calculations.
00:35
Okay, once we have these venn diagrams, we should immediately give some numbers or some parameters to the two individual areas to keep track of the calculations.
00:48
Okay, so we have a many students here, b many students here, c, d, e, f, g.
00:58
Okay now let us keep reading the problem.
01:03
Before i actually we need to write the following.
01:07
We have all these numbers added together a b c d e f g this must be equal to 500 because everybody prefers a subject so there is no one outside.
01:25
Okay now let us continue reading.
01:27
We have 300 of them preferring to study chemistry.
01:32
So we have d plus e plus f plus g equal to 300.
01:41
And we have 275 of them preferring to study mathematics.
01:47
So we have a plus b plus d plus e equal to 275.
01:55
And 225 prefer to study physics.
02:00
B plus c plus e plus f equal to 225.
02:08
Okay, 150 of them prefer to study chemistry and mathematics.
02:14
So we are here.
02:16
Here d plus e equal to 150.
02:23
85 of them want to study mathematics and physics.
02:28
So we are here e plus e equal to 85.
02:35
And 120 of them want to study chemistry and physics.
02:41
So we are here e plus f equal to 120.
02:46
So we are going to find out the number of students who study some certain cases and we are going to answer them.
02:56
But before that, let us solve this system of equations...