Problema Solution
Two mathematics classes took the same test. The mean of the first class of twenty students was 90%. The mean of the second class was 75%. If the mean grade for the combined classes was 81%, how many students were in the second class?
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Lets assume that the total number of points per test is 100 then
the first class had 20 students and a mean of 90%
lets 'a' = that the sum of all scores in the first class
a/20 = 90
a = 20*90
a = 1800
lets say that the second class has 'x' students and a mean of 75%
lets 'b' = that the sum of all scores in the second class
b/x = 75 => b = 75x
the mean grade for the combined classes was 81%
(a + b)/(29 + x) = 81
plug a = 1800 and b = 75x into the last equation
(1800 + 75x)/(29 + x) = 81 multiply both sides by (29 + x)
(1800 + 75x) = 81(29 + x)
by solving the equation we find
x = 30 students
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there were 30 students in the second class.