The total number of students in section A and B of a class is 200. The number of students in section B is 40 less than that of section A. The average score of the section B, in a test is 20% more than that of students in A. If the average score of all the students in the class is 48.6, what is the average score of the students in A?
Options:
38
40
45
36
49
Answer (2)
Let's solve this problem step-by-step:
Let the number of students in section A be x . Therefore, the number of students in section B will be x − 40 since it is 40 less than section A.
According to the problem, the total number of students in both sections is 200. So, we have: x + ( x − 40 ) = 200 Simplifying this, we get: 2 x − 40 = 200 2 x = 240 x = 120 So, there are 120 students in section A.
Since section B has 40 fewer students than section A, the number of students in section B is: 120 − 40 = 80
Now, let's consider the averages. Let the average score of the students in section A be a . Then the average score of the students in section B is 20% more, which would be: a + 0.2 a = 1.2 a
The total average score for all students in both sections is given as 48.6. We can set up an equation for the total average: 200 120 a + 80 ( 1.2 a ) = 48.6 Simplify and solve this equation: 200 120 a + 96 a = 48.6 200 216 a = 48.6 1.08 a = 48.6 a = 1.08 48.6 a = 45
Therefore, the average score of the students in section A is 45 .
The correct multiple choice option is: 45 .
The average score of the students in section A is 45. This was determined by first calculating the number of students in each section and then deriving the average based on the total average score. The chosen multiple-choice option is 45.
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