A survey of 80 students found that 40 students preferred biology, 24 preferred chemistry, and 16 preferred physics. If there are 200 students in the whole school, how many are expected to prefer biology?
Let’s begin looking at the survey. There were 80 students in the survey. And 40 of them preferred biology. So in this survey, 40 out of the 80 students preferred biology. And if we’ll reduce that, because both numbers are divisible by 40, we get one-half. So from the survey, we should expect that half of the student body should prefer biology.
In the whole school, there are 200 students. So from the survey, we expected one-half of whatever the total would be to prefer biology. So if there are 200, we know that half of that is 100. But how did we get 100? Well, that’s because you take the total number of 200 and multiply by the one-half. So we could put 200 over one. And we have one fraction times one fraction. And we could simplify because two goes into 200 and get 100 over one, which is just 100.
So if there are 200 students in the whole school, we would expect 100 students to prefer biology.