Here's what I'm trying to find, any help would be appreciated.

188 students took a test; 52 males and 136 females.
The average score for all 188 students is 90.1%
The average score for the 52 males is 79.2%
What is the average score for the 136 females?

This is a real problem that Mrs. Blufinz is trying to work out and asked for my help. I promise to give credit to anyone that can assist.
(gratuitous watch pic)

 

94.3%

Women are smarter

188*.901=52*.792+136*x

 

Thanks Taddy

 

I'm curious what class has so many more women than men. In my field, it's often the opposite.

 

It doesn't take a math problem to figure this out.

 

My wife works for a large Canadian Insurance Company and manages a large group of quality assurance agents, who review long-term disability claims. The numbers were 188 disability claim reviews, 52 on the West Coast offices and 136 in the East Coast Offices. She knew that the west coast offices had an average of score of 79.2% for their claims reviews (not good), and needed to know the east coast average.

I substituted student scores for claims reviews, as it was easier to state. Same numbers, same problem.

Turns out East Coast Long-Term Disability Claims reviewers are better than their West Coast counterparts.

 

94.27 (if you round it). You have to weight the averages.
The males account for 52/188ths of the total and the females account for 136/188ths of the total.
Or the males account for 27.65% of the average and the females account for 72.34%.
Using that you come up with the formula (79.2*.2765)+(X*.7234)=90.1.
That translates to 21.8988 + (X*.7234)=90.1.
Which becomes (X*.7234)=90.1-21.8988.
Which becomes (X*.7234)=68.2012.
Which becomes X=(68.2012/0.7234)
which = 94.27

If you work it up in a spreadsheet by trial and error the accurate number is 94.26765

 

and I agree with Bluf....the boys better hit the books

 

Thank you