how do you sove this?

G

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An instructor for a physics class has posted the scores for his final grades.

#students Mean score Mean grade
Freshman 43 76 C
Sophomore ? 88 B+
Junior 58 81 B-
Senior 26 75 C

If the mean score for all students was 81, how many sophomore students were in the class?



(all of the above is one problem, but when I added up the scores, I did not get 81, did the teacher make a mistake? or did I misinterpret data?) Please help!! I know it's all probably obvious :cry:
 
For clarity, below is a reformatting of the table:

Code: 
|-----------|----------|-------|-------|
|           | num. of  | Mean  | Mean  |
|           | students | score | grade |
|-----------|----------|-------|-------|
| Freshman  |    43    |  76   |   C   |
| Sophomore |     ?    |  88   |   B+  |
| Junior    |    58    |  81   |   B-  |
| Senior    |    26    |  75   |   C   |
|-----------|----------|-------|-------|
Eliz.
 
Hint: What was the total number of points earned by freshman? By juniors? By seniors? What is the total number of students other than sophomores? If there are "x" sophomores earning, on average, 88 points each, what does "x" need to be for the average of all the students to be the given overall mean value?

If you get stuck, please reply showing all of your steps.

Eliz.

P.S. The reformatting of the table was provided as a courtesy to other users, so they would be able to read what you'd posted. I apologize for any confusion.
 
Thanks for the table, it was easier to understand, not sure how to use all functions , 1st time using this site. okay, I figured this out so far, but what formula do I use to solve it and where are things plugged in?

total score fresh=3268
total score junior=4698
total score senior=1950

the total # of students other than soph. is 127, but I still don't know total points or total
I keep coming up with formulas that have 2 unknown #'s and can't solve them
I hate not seeing the obvious what's the formula so I can kick myself, please help!
 
cookie2 said:
total score fresh=3268
total score junior=4698
total score senior=1950

the total # of students other than soph. is 127...
Click to expand...
That's a good start. Now pick a variable for the number of sophomores. Add that to the total.

How many points did they get? Add that to the other total.

Create the "average" expression. Set equal to the given average. Solve.

Eliz.
 
it's obvious to me now..

43*76+X*88+58*81+26*75=81(127+X)

3268+88X+4698+1950=10287+81X

88X+9916=10287+81X

7X+9916=10287

7X=371

7X/7=371/7

X=53 students :!: :lol:
 
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