Problem Solving

The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?


A. 2x - 8
B. x - 4
C. 8 - 2x
D. 16 - x
E. 8 - x/2


A

x= average

10x = the total score for all students

total score for 5 students with an average of 8 is 5 * 8 = 40

10x-40 is the total score for the 5 remaining students

(10x-40)/5 = average of the remaining 5 students

2x-8 = average

bacali wrote:The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?


A. 2x - 8
B. x - 4
C. 8 - 2x
D. 16 - x
E. 8 - x/2


A

x= [ 5*8 + (total marks of 5 students)]/ 10

5* 8 would be total marks of 5 students whose marks are known

10x-40= total marks of 5 students

hence average= 10x-40/5

=2x-8

IMO A

This is weighted average concept.


Let k be the average of the 5 students that we need to find

Average mark x is =

5*8 + 5 * k / 10 = x

40+5k = 10x
8+k=2x
k=2x-8

A)

I backsolved this one. So..

For the average score of the REMAINING 5 students I chose 9. The average of the total 10 students would be:

Average of first 5 students: 8 which is 5 * 8 = 40
Average of remaining 5 students 9 which is 5 * 9 = 45

So the average for all 10 students is 85/10 or 8.5. Thus our x is 8.5.

Starting with the answer choices we substitue 8.5 with x to see which answer choice will give us 9 as the answer. (Average of remaining students):

A. is the only solution that gives us 9.

2(8.5) - 8 = 17 - 8 = 9.

I backsolved as well..

If half of the students scores averaged 8, pretend the other half averaged 12 so that x = 10, an easy number to work with. Solve each of the equations with x = 10 and see which answer gives you 12 as a solution.


A. 2(10) - 8 = 12 < YES
B. (10) - 4 = 6
C. 8 - 2(10) = -12
D. 16 - (10) = 6
E. 8 - (10)/2 = 3