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

Answer:

The C) statement is true.

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:

$x=\frac{x_1*18+x_2*24}{18+24}\\x=\frac{84*18+x_2*24}{42}\\x=\frac{1512+x_2*24}{42}$

Since the average is given by $Average=\frac{Sum of all values}{Amount of values}$. 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:

$x=\frac{1512+2400}{42}\\x=93$

for it's maximun value and

$x=\frac{1512+0}{42}\\x=36$

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