Help!!!

[ch2831]

Aisha, Ben and Cheng entered a weekly school competition. In each week, the three of them came first second and third in some order. The scores for the top 3 places are positive integers and the same each week. The score for first place was more than the score for second place which was more than the score for third place. Aisha won in the first week. At one stage the total score for Aisha was 12, for Ben was 34 and for Cheng 9. How many weeks did they take to achieve these scores?

 

[wjm11]

Aisha, Ben and Cheng entered a weekly school competition. In each week, the three of them came first second and third in some order. The scores for the top 3 places are positive integers and the same each week. The score for first place was more than the score for second place which was more than the score for third place. Aisha won in the first week. At one stage the total score for Aisha was 12, for Ben was 34 and for Cheng 9. How many weeks did they take to achieve these scores?

To start, let’s figure out how many total points were awarded when Aisha had 12, Ben 34, and Cheng 9: 12 + 34 + 9 = 55. Possible point allocations for first, second, and third place could be something like:

3 + 2 + 1 = 6
or
4 + 2 + 1 = 7
or
4 + 3 + 1 = 8
and so on.

The total of 55 must be evenly divisible by whatever the point allocations add up to. Does that make sense? The total points awarded each week (6, 7, 8, … whatever) times the number of weeks must equal 55.

You should be able to figure it out from here.