Aisha, Ben and Cheng enter a school weekly competition. They earn 8 points for coming first, 2 points for coming second and 1 point for coming third. In each week, they come first, second and third in some order. After 5 weeks, the total score for Aisha was 12, for Ben was 34 and for Cheng 9. What is the smallest number of additional weeks for them to all have the same score?

Question

inkyvoyd · Answer

Do you need an system setup?

kropot72 · Answer

Let x = the final score for each contestant
The additional total number of points needed to equalise the scores is:
(x - 12) + (x - 34) + (x - 9) = 3x - 55
(3x - 55) must equal a multiple of 11 the reason being that the total weekly points = 11.
Also the solution for x must be an integer and be greater than any of the 5 week scores. The lowest multiple of 11 that meets these requirements is 77.
3x - 55 = 77
3x = 132
x = 44
It will take 12 weeks to reach a score of 44 for each contestant.
The smallest number of additional weeks = 12 - 5 = 7 weeks