COMPASS Math Test Problem (Pre-Algebra)?
I didn't sleep yesterday, so I asked my adviser if I could retake it. There was a certain question that took average test scores from two classes and then averaged them together. It gave the numbers (averages). It then asked what the ratio was of students taking the test were from class one to class two. Ex: 1:5 1:7 3:5 etc. At first I didn't really understand the emphasis of the ratio. I knew from looking at the numbers that adding them together and averaging wouldn't give me the same number they were using as the average from both classes.
Can you give me a real example of this type of question and explain how it is done? It seems very obscure to me. I don't know how to find it via search engine.
Answers & Comments
Verified answer
Class1 has 20 students, and their average score was 80 points.
Class2 has 30 students, and their average score was 70 points.
The average score for the two classes was (20*80 + 30*70)/(20 + 30) = 74
which, as you say, is not simply the average of the two averages.
You say you're pre-algebra, so I can't use algebra to show you how such a problem is done. Sorry, but I'm going to have to use a little algebra.
Suppose class1 has m students and class2 has n students, where m and n are positive integers. Suppose we know that class1's average was 80, class2's average was 70, and the combined average was 74. We want to find m/n.
We have
(80*m + 70*n)/(m+n) = 74
Multiply both sides by (m+n):
80*m + 70*n = 74(m + n) = 74*m + 74*n
Subtract 74*m from both sides:
6*m + 70*n = 74*n
Subtract 70*n from both sides:
6*m = 4*n
Divide both sides by 6:
m = 4*n/6 = (2/3)n
Divide both sides by n:
m/n = 2/3
So the ratio of the number of students in class1 to the number of students in class2 is 2:3.
If you want something like a formula, the ratio is (74 - 70)/(80 - 74). For a general problem, replace the 74's with the combined average; replace the 80 with the average of the first class; and replace the 70 with the average of the second class.