Question 1205574
.
In a math class 40% are girls. The average score for the girls was 82.3% 
while the average score for the boys was 72.5%. 
What was the average score of all the students.
~~~~~~~~~~~~~~~~~~~~~


<pre>
We may think that the class is 25 students, in all,
of which 40%, or 10 students, are girls and the rest, 25-10 = 15 students, are boys.


Then the total score of girls is 10*82.3, while the total score of boys is 15*72.5.


Then the total score of the class is  10*82.3 + 15*72.5 = 1910.5.


Hence, the average score of the class is  {{{1910.5/25}}} = 76.42.


    Notice that this number 76.42 is the same as  0.4*82.3 + 0.6*72.5 = 76.42.


    So, we could get the answer using this simple formula (!)



<U>ANSWER</U>.  The average score of all the students in the class is 76.42.
</pre>

Solved.