SOLUTION: In a math quiz, the average score of a class of 28 students is 82. The average of those who passed was 88, while the average of those who failed was 67. How many students in the cl

Algebra ->  Average -> SOLUTION: In a math quiz, the average score of a class of 28 students is 82. The average of those who passed was 88, while the average of those who failed was 67. How many students in the cl      Log On


   

Question 1105867: In a math quiz, the average score of a class of 28 students is 82. The average of those who passed was 88, while the average of those who failed was 67. How many students in the class failed the test?
Found 2 solutions by rothauserc, greenestamps:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the number of students who passed and y be the number of students that failed
:
1) x + y = 28
:
2) 88x + 67y = 82*28
:
solve equation 1 for x
:
x = 28-y, substitute for x in equation 2
:
88(28-y) +67y = 82*28
:
2464 -88y +67y = 2296
:
-21y = -168
:
y = 8
:
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eight students failed the test
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:

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of students who passed and y be the number who failed.

(1) x%2By=28 the number of students is 28

(2) 88x%2B67y+=+82%2A28 the class average was 82

We want to solve for y, so eliminate x. Multiply equation (1) by 88 and subtract equation (2):

88x%2B88y+=+88%2A28
88x%2B67y+=+82%2A28
21y+=+6%2A28+=+168
y+=+8

8 students failed the test.

Here is a very different way to solve "average" or "mixture" problems, without algebra.

matrix%283%2C3%2C88%2C%22%22%2C15%2C%22%22%2C82%2C%22%22%2C67%2C%22%22%2C6%29

In this diagram, the averages of those who passed and those who failed are in the first column, and the overall average is in the second column. The numbers in the third column are the differences, calculated diagonally, between the numbers in the first and second columns.

When the numbers are displayed this way, the numbers in the third column show the ratio between the numbers of students in the two groups.

That ratio is 15:6, or 5:2. That means 5/7 of the students passed and 2/7 of them failed. And 2/7 of the total of 28 students is 8, so the number of students who failed is 8.