sandy wrote:
There are 32 students in Jamie’s eighth-grade class. Each student took a 50-point test; the class average (arithmetic mean) was 82% correct. The teacher has assigned one 4-point, extra-credit question. How many students will need to answer the extra-credit question correctly in order to bring the class average to 86% correct?
A. 15
B. 16
C. 17
D. All of the students
E. It will not be possible for the class to reach an average of 86% correct.
We can create the equation:
(0.82(50)(32) + 4x)/32 = 0.86(50)
0.82(50)(32)/32 + 4x/32 = 0.86(50)
41 + x/8 = 43
x/8 = 2
x = 16
Alternate Solution:
Each test point is worth 2%. Thus, the extra credit question is worth 4 points, or 8%. If all 32 students answered it correctly, then the class average would increase by 8%. Since we want to increase the class average by only 4%, then only half of the students (i.e., 16 students) need to answer it correctly.
Answer: B