Question

A teacher gives a test to two algebra classes. The first class has 18 students, and the second has 24 students. If the average for the first class is 84% and x is the overall average grade for all students, then which of the following statements is true? A) 84≤X≤93.1B) 42≤X≤92C) 36≤X≤93.1D) 36≤X≤92E) 42≤X≤84

Answer 1

The C) statement is true.

Step-by-step explanation:

Let's call
`x_1` the average for the first class and
`x_2` the average for the second class. The overall average x is then:

`x=(x_1*18+x_2*24)/(18+24)\\x=(84*18+x_2*24)/(42)\\x=(1512+x_2*24)/(42)`

Since the average is given by
`Average=(Sum of all values)/(Amount of values)`. We can now calculate x assuming the maximun and minimun values of
`x_2`, 2400 (which is 100 times 24) and 0 respectivly. That gives:

`x=(1512+2400)/(42)\\x=93`

for it's maximun value and

`x=(1512+0)/(42)\\x=36`

for it's minimun value. So we get that x is between 36% and 93%.