SOLUTION: A physical education class has three times as many girls as boys. During a class basketball game, the girls average 18 points each and the class as a whole average 17 points per pe

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Question 641778: A physical education class has three times as many girls as boys. During a class basketball game, the girls average 18 points each and the class as a whole average 17 points per person. How many points does each boy score on average?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = the number of boys
Then the number of girls = 3b
The girls average will be the total points scored by girls (G) divided by the number of girls:
G/3b = 18
The class average will be the number of points scored by girls (G) plus the
number scored by boys (B) divided by the total numer of students:
(G + B)/(3b + b) = 17
But the number of points scored by boys = ab where a = the boys' average
From the 1st equation, G = 54b
(54b + ab)/4b = 17
We can cancel b from numerator and denominator:
(54 + a)/4 = 17
54 + a = 68
a = 14
So the boys average = 14