Pre-Algebra Placement Test problem

• Nov 5th 2010, 11:54 AM
Aravsion
Pre-Algebra Placement Test problem
I'm preparing for college and I got stuck on one of the problems of Pre-Algebra Placement Test.. So can someone please help me find the solution to it.

A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?
• Nov 5th 2010, 12:08 PM
pickslides
You have $\displaystyle n_j = 35, n_s = 15, \bar{x}_j = 80 , \bar{x}_s = 70$

Working backwards with the formula for the mean i.e. $\displaystyle \bar{x} = \frac{\sum x}{n}$

$\displaystyle \displaystyle\bar{x}_j = \frac{\sum x_j}{n_j}\implies 80 = \frac{\sum x_j}{35}\implies \sum x_j = 80\times 35$

$\displaystyle \displaystyle\bar{x}_s = \frac{\sum x_s}{n_s}\implies 70 = \frac{\sum x_s}{15}\implies \sum x_s = 70\times 15$

Now for the mean of both (the total)

$\displaystyle \displaystyle\bar{x} = \frac{\sum x_j+\sum x_s}{n_j+n_s} = \frac{80\times 35+70\times 15}{35+15}= \dots$
• Nov 5th 2010, 09:32 PM
CaptainBlack
Quote:

Originally Posted by Aravsion
I'm preparing for college and I got stuck on one of the problems of Pre-Algebra Placement Test..

What is the purpose of a Pre-Algebra Placement Test?

CB
• Nov 7th 2010, 01:33 PM
Aravsion
Quote:

Originally Posted by CaptainBlack
What is the purpose of a Pre-Algebra Placement Test?

The purpose is to prepare for college. The problems I've done in like 8 or 9 grade I forgot how to do and its all thanks to the education we get here in U.S. schools. (Smile)
So, that is why so many people in school have problems with mathematics and second grade problems.