An average mark is computed for 100 students in Business, an average is computed for 300 students in Arts, and an average is computed for 200 students in Science. The average of these three averages is 85%. However, the overall average for the 600 students is 86%. Also, the average for the 300 students in Business and Science is 4 marks higher than the average for the students in Arts. Determine the average for each group of students by solving a system of linear equations.
Let $x,y,z$ represent the students in business, arts and science respectively.
$\frac{1}{6}x+\frac{3}{6}y+\frac{2}{6}z=0.85$
$\frac{1}{3}x+\frac{1}{3}y+\frac{1}{3}z=0.86$
$\frac{1}{6}x-y+\frac{1}{3}z=0.04$
But when I solve for these 3 equations I end up getting $x=0.48666$,$y=0.54666$, and $z=1.51666$, which I dont believe is correct.
I believe that some of my equations are wrong, could someone tell me which one? Thanks a lot!
The first equation should be the average of the three averages, so it should not be weighted: the correct form is $\frac{1}{3}x + \frac{1}{3}y + \frac{1}{3}z = 0.85$.
The second is the overall average, so it is weighted. Basically, it is your first equation set equal to $0.86$.
I believe the third equation is correct. I would like to remark though, that x, y and z represent the averages, not the students.