36 students took a final test in math.the average score of those who passed was 78, while the average score of those who failed was 60.the average of all the scores was 71. how many of the students passed?
number passed ---- x
number failed ------ 36-x
sum of scores of passers = 78x
sum of scores of failures = 60(36-x)
78x + 60(36-x) = 71(36)
solve for x
thanx
To find out how many students passed the final test, we can use the information given.
Let's assume that P represents the number of students who passed and F represents the number of students who failed.
We know that the average score of those who passed was 78, and the average score of those who failed was 60. We also know that the average of all the scores was 71.
To find the number of students who passed, we need to calculate the sum of their scores and the sum of the scores of those who failed. Then we can use this information to solve the equation.
The sum of the scores of the students who passed is P * 78, and the sum of the scores of the students who failed is F * 60. The average of all the scores is the sum of the scores of all the students divided by the total number of students, which is (P * 78 + F * 60) / 36.
We also know that the average of all the scores is 71, so we can set up the equation:
(P * 78 + F * 60) / 36 = 71
Now we can simplify the equation:
(P * 78 + F * 60) = 36 * 71
Next, we can solve this equation to find the values of P and F.
Unfortunately, we don't have enough information to solve this equation. We need either the value of P or F to find the other one.