Question

In a different test, the mean score of 50 students is 54%

The students are split in two groups. Group A and Group B.
The mean score for Group A is 60% and the mean score for Group B is 50%
How many students are in Group B and how many are in Group B?

Answer 1

Group A has 20 students

Group B has 30 students

Explanation:

The mean score of 50 students is 54%, so the sum of 50 scores, divided by 50 is 54%. That means that 50(0.54) = 27 points were scored between the 50 students.

Let x represent the number of students in Group A

Let y represent the number of students in Group B

We have

0.6x + 0.5y = 0.54(50) (the points scored, times their averages is the total)

and

x + y = 50

Use substitution to solve...solve the second equation for one variable...

x = 50 - y

Now plug that into the first equation...

0.6(50 - y) + 0.5y = 27

30 - 0.6y + 0.5y = 27

-0.1y = -3

y = 30

So there are 30 students in group B, therefore there are 20 students in group A