Average Them All

Probability Level 2

The 12th graders in school A have the average score in math exam of 66 while the ones in school B have the average of 73.

If the average score of all students is 70, and the difference of numbers of students between the two schools is 10, what is the total number of students in both schools?


The answer is 70.

Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

Let x x be the number of students in school A and y y be that of school B.

66 x + 73 y x + y = 70 \dfrac{66x+73y}{x+y}=70

66 x + 73 y = 70 x + 70 y 66x+73y= 70x+70y

Thus, 3 y = 4 x 3y=4x .

If y = x + 10 y=x+10 , then 3 ( x + 10 ) = 4 x 3(x+10)=4x . Hence, x = 30 x=30 .

If y = x − 10 y=x-10 , then 3 ( x − 10 ) = 4 x 3(x-10)=4x ; x = − 30 x=-30 , which is not applicable.

Therefore, x + y = 30 + 40 = 70 x+y=30+40=\boxed{70} .

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