How to solve my math word problem

Question

To mathematic classes Took the same test the mean of the first class was 20 students was exactly90% the mean of the second class of 75% if the mean grade for the combine classes was 81% how many students were in the second class

Answer 1

Average = sum / number of pieces of data......cross multiply and get

Average * number of pieces of data = sum of data.

 

So 20 students averaging 90 means that the 20 pieces of data added up to 1800.

if the second class has n students and averages 75, then the sum of the n students is 75n.

 

The combined classes therefore can be represented as follows:

The number of students in both classes is n+20.

the sum of all the scores is 1800 + 75n

the combined average is 81...........so

 

81(n + 20) = 1800 + 75n

81n + 1620 = 1800 + 75n

6n              = 180

n                =  30

 

Hope this helps

n                = 30

Answer 2

Let's call them class A and B.

 

To compute the average for class A, we would add up the total of their scores, T(A) and divide it by the number of students in the class:

 

.9 = T(A) / 20

 

Similarly, for class B we would get:

 

.75 = T(B) / X

 

Lastly, for class C we would get:

 

.81 = T(A +B) / (20 + X)

 

Notice that T(A + B) = T(A) + T(B), both of which you can solve for by rearranging the first two equations.  Then just solve for X!