40 students played a game.
The score was either two points, four points, six points or ten points.
There were four people who had two points and eight people who had ten points.
The average score was 5.8 points.
Find the number of people who had four points and six points.
Answer
Four points : 12 persons
Six points : 16 persons
Solution
The total score is 5.8 × 40 = 232.
Total score of 2 points and 10 points is 2 × 4 + 10 × 8 = 88.
Total score of 4 points and 6 points is 232 - 88 = 144.
Total number of people of 4 points and 6 points are 40 - (4 + 8) = 28.
Therefore number of people of 6 points is (144 - 4 × 28)/(6 - 4) = 16.
Number of people of 4 points is 28 - 16 = 12.
The score was either two points, four points, six points or ten points.
There were four people who had two points and eight people who had ten points.
The average score was 5.8 points.
Find the number of people who had four points and six points.
Answer
Four points : 12 persons
Six points : 16 persons
Solution
The total score is 5.8 × 40 = 232.
Total score of 2 points and 10 points is 2 × 4 + 10 × 8 = 88.
Total score of 4 points and 6 points is 232 - 88 = 144.
Total number of people of 4 points and 6 points are 40 - (4 + 8) = 28.
Therefore number of people of 6 points is (144 - 4 × 28)/(6 - 4) = 16.
Number of people of 4 points is 28 - 16 = 12.
