Students at Linear University write a linear algebra examination. An average mar

Question

Students at Linear University write a linear algebra examination. An average mark is computed for

200 students in business, and average is computed for300students in liberal arts, and an average is computed for100

students in science. The average of these three averages is 83%.

However, the overall average for the 600 students is80%

Also, the average for the 300 students in business and science is 4 marks higher than the average for the students in liberal arts. Determine the average for each group of student by solving a system of linear equations.

Explanation / Answer

Dear Student Thank you for using Chegg !! Let us assume Average of students in business = x Number of students in business = 200 Average of students in liberal art = y Number of students in liberal art = 300 Average of students in Science = z Number of students in Science = 100 also given (x + y + z / 3) = 83 (x + y + z ) = 249 (1) (200x + 300y + 100z)/600 = 80 (2x + 3y + z) = 480 (2) (x + z ) / 2 = y + 4 x - 2y + z = 8 (3) (2) - (1) x + 2y = 231 (4) (1) - (3) 3y = 241 y = 80.33333 x = 70.33333 z = 98.33333 Hence we know the 3 averages Solution

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