SOLUTION: Hi In a class of 40 the average score was 70.25. The average scores for boys and girls were 68 and 73 respectively. How many boys were in the class. Thanks

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Question 1176443: Hi
In a class of 40 the average score was 70.25. The average scores for boys and girls were 68 and 73 respectively. How many boys were in the class.
Thanks
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
In a class of 40 the average score was 70.25.
The average scores for boys and girls were 68 and 73 respectively.
How many boys were in the class.
~~~~~~~~~~~~~~~~ 


Let x be the number of boys;

then the number of girls is  (40-x).


Total scores of boys is 68x;  total scores of girls is 73*(40-x).


Total scores of the class is 40*70.25 = 2810.


The equation of total scores is


    68x + 73*(40-x) = 2810.


From the equation


    x =  = 22.


ANSWER.  There are  22  boys in the class.

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The other tutor has provided a good solution using the standard formal algebraic method for solving problems like this.

This, and a large number of other types of problems, can be seen as a weighted average problem, or a mixture problem. Problems like that can be solved by seeing where the weighted average lies between the two given averages.

Consider the overall (weighted) average and the averages of the boys and girls on a number line: 68, 70.25, and 73.

With simple arithmetic, determine that the class average lies 2.25/5 = 9/20 of the way from 68 to 73.

That means 9/20 of the students in the class are girls.

9/20 of 40 is 18, so there are 18 girls in the class; that means 22 boys.
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