Question

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. what is the smallest number of additional weeks that will allow them to have the same score?

Answer 1

The minimum possible total weekly score is 3 + 2 + 1 = 6
The total score for the three people at one stage = 12 + 34 + 9 = 55
The factors of 55 are 5 * 11. The minimum weekly score must therefore be 11 since 5 is too small. Therefore 5 weeks were taken to achieve the scores.

Answer 2

thx man now plz answer the moddified question

Answer 3

The equal total score must be a number that has 3 and 11 as a factor. 66 is such a number but this gives a score of 22 each which is less than Ben's score after 5 weeks.
The next possible total score is 99. This gives a score of 33 each which is still too small.
By repeating this process it is found that a total score of 132 meets the requirements. This score takes 12 weeks to achieve.
The smallest number of additional weeks is 12 - 5 = 7 weeks

Answer 4

thx man ur the best "FAN" xD