SOLUTION: Hello, Here is the 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 cla

Algebra ->  Probability-and-statistics -> SOLUTION: Hello, Here is the 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 cla      Log On


   

Question 998777: Hello,
Here is the 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≤93.1
B) 42≤X≤92
C) 36≤X≤93.1
D) 36≤X≤92
E) 42≤X≤84
(I don't know how to solve for the numbers)
Found 2 solutions by macston, KMST:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
The sum of scores for first class:
18*84=1512
.
LOWEST POSSIBLE AVERAGE:
If average of second class=0, sum of scores for second class:
24*0=0
And combined average:
(1512+0)/42=36
The lowest average will be 36.
.
HIGHEST POSSIBLE AVERAGE:
If the average of the second class=100, sum of scores for second class:
24*100=2400
And combined average:
(1512+2400)/42=93.14
The highest average will be 93.14
.
So the possible average range will be:
36 < Average < 93.14
.
So the correct answer is (C).

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%2818%2A84%2B24%2A0%29%2F42%3C=x%3C=%2818%2A84%2B24%2A100%29%2F42
1512%2F42%3C=x%3C=3912%2F42
Since 3912%2F42=92.143 (rounded),
an average grade of 3912%2F42 would be reported as 93.1 .
So, 36%3C=x%3C=93.1 .

EXPLANATION:
The total number of students taking the test is
18%2B24=42 .
Maybe every student in the second class got %220%25%22 on the test.
In that case, the sum of all the test grades is
18%2A%2284%25%22%2B24%2A%220%25%22=18%2A%2284%25%22 , and the average grade for all students is
18%2A%2284%25%22%2F42=%2236%25%22 .
So you would say x=36 .
Probably the second class did better that that, and x%3E36 .
Maybe every student in the second class got %22100%25%22 on the test.
In that case, the sum of all the test grades is
18%2A84%2B24%2A100=18%2A84%2B2400=3912 , and the average grade for all students is
3912%2F42=93.143 (rounded).
So you would say x=92.1 .
However, most likely not every student in the second class got 100%,
so the sum of the grades would be less than 3912 ,
and the average would probably be less than 93.1 .