I'm just curious at to creating the system of linear equations for the certain conditions given by this question.
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.
So far this is what I have (although not sure if correct)
Let $x_1,x_2,x_3$ represent the students in business, arts and science respectively.
$100x_1+300x_2+200x_3=86$
$100x_1+200x_3+4=300x_2$
Im not sure as to how to create an equation for the first one.
Thanks for the help!
$x$ = average business
$y$ = average arts
$z$ = average science
Just to say, the difference between the 85 and 86 equations is that the 85 represents nonweighted averages, while the 86 is weighted.
Since you only want business to have 1/6 weight in the actual weighted average, you multiply it by 1/6. This is a slight problem with your first equation.
$$\frac{1}{6}x + \frac{3}{6}y + \frac{2}{6}z = 0.86$$ (weighted average)
For the final equation, you can
For the average of averages, you just take the raw average
$$\frac{x+y+z}{3} = 0.85$$
For the last one, we do another weighted average; however, this time, we are just weighting the business and science components. Because business makes up 100 of the 300 people in the field, we do 1/3, and for science, 2/3
$$\frac{\frac{1}{3}x+\frac{2}{3}z}{2} - y = 0.04$$
To find the final answer, eliminate the z to get a two variable, two equation system of equations.