In a group of 48 students that recently took a math test, the average score was 90 points. Some of the students received a score of 100 points, and 20 students each received a score of 80 points, and all the others received 90 points each. How many students received a grade of 100 points?
+23254 Let x = number of students who got 100
Let y = number of students who got 90
Let z = number of students who got 80 ---> z = 20
Number of students:
x + y + z = 48 ---> x + y = 28 (since z = 20)
Points: 100x + 90y + 80z = 48(90) (since the average for 48 students was 90 points each)
100x + 90y + 80(20) = 4320
100x + 90y = 2720
Putting these two equation together:
x + y = 28 ---> (multiply by 90) ---> 90x + 90z = 2520
100x + 90y = 2720 ---> (change signs) ---> -100x - 90y = -2720
Adding down the columns: -10x = -200
x = 20
Since x + y = 28 ---> y = 8
+23254 Let x = number of students who got 100
Let y = number of students who got 90
Let z = number of students who got 80 ---> z = 20
Number of students:
x + y + z = 48 ---> x + y = 28 (since z = 20)
Points: 100x + 90y + 80z = 48(90) (since the average for 48 students was 90 points each)
100x + 90y + 80(20) = 4320
100x + 90y = 2720
Putting these two equation together:
x + y = 28 ---> (multiply by 90) ---> 90x + 90z = 2520
100x + 90y = 2720 ---> (change signs) ---> -100x - 90y = -2720
Adding down the columns: -10x = -200
x = 20
Since x + y = 28 ---> y = 8
