Problema Solution
on a recent math test, the boys averaged 81 and the girls averaged 90. if there are twice as many boys in the class as girls, what was the overall average for the class?
Answer provided by our tutors
Let
x = the number of boys
t1 = sum of all the grades of each boy
y = the number of girls
t2 = sum of all the grades of each girl
the boys averaged 81 that is
t1/x = 81 => t1 = 81*x
the girls averaged 90 that is
t2/y = 90 => t2 = 90*y
there are twice as many boys as girls:
y = 2*x
the overall average of the class is
(t1 + t2) / (x + y) = (81*x + 90*y) / (x + y) = (81*2*y + 90*y) / (2y + y) = 252 / 3 = 84
The overall average of the class is 84.