SOLUTION: Hi. there are 2 classes with an average of 62. One class of 36 students has an avg of 50 and the other class has an avg of 80. How many students are in the other class? I know

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Question 1004368: Hi.
there are 2 classes with an average of 62. One class of 36 students has an avg of 50 and the other class has an avg of 80. How many students are in the other class?
I know the answer is 24 but I am not sure why.
Can someone please tell me the steps to solve this.
Thanks.
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Hi.
there are 2 classes with an average of 62. One class of 36 students has an avg of 50 and the other class has an avg of 80. How many students are in the other class?
I know the answer is 24 but I am not sure why.
Can someone please tell me the steps to solve this.
Thanks.
Let number of students in the other class, be N

Then total scores for this class is: 80N

Total scores for 36-student class: 36(50), or 1,800

Total number of students in both classes = N + 36

We then get the following SCORES equation: 80N + 1,800 = 62(N + 36)

80N + 1,800 = 62N + 2,232

80N – 62N = 2,232 – 1,800

18N = 432

N, or number of students in other class = 432%2F18, or highlight_green%2824%29

Answer by ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
.
there are 2 classes with an average of 62. One class of 36 students has an avg of 50 and the other class has an avg of 80. How many students are in the other class?
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One class of 36 students has an avg of 50.
So, their scores are 36*50 = 1800 in total.

The second class of x (unknown) students has an avg of 80.
So, their scores are x*80 = 80x in total.

The scores for both classes are 1800 + 80x.
The number of students in both classes is (36+x).

The average score for two classes is %281800%2B80x%29%2F%2836%2Bx%29.
It is equal to 62.

So, your equation is

%281800%2B80x%29%2F%2836%2Bx%29 = 62.

Solve it for x.

1800 + 80x = 62*(36+x),
1800 + 80x = 2232 + 62x
80x - 62x = 2232 - 1800,
18x = 432,

x = 432%2F18 = 24.