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Mathematics
OpenStudy (anonymous):

Aisha, ben and Cheng entered a weekly school competition. Ineach week they participated, the three of them came, first, seconf and third in some order. The scores forthe top three places were positive integers and the same each week. The scorefor the first place was more thanthe score for the second place which was more than the score forthe third place. Aisha won in the first week. at one stage the score for A was 12, for Ben it was 34 and for Cheng 9. how many week(s) did it take to achieve these scores? Determine all scores in this time After some more weeks, Aisha, Ben and Cheng had the same score> What is the smallest number of additional weeks that will allow them to have the same score?

OpenStudy (anonymous):

Maths Challenge??

OpenStudy (anonymous):

Yes. :)

OpenStudy (anonymous):

:D same!! stuck on that too:( so hard...

OpenStudy (anonymous):

Which ones have you done?

OpenStudy (anonymous):

if you get the answer will you pls. teel and if i get the answer ill tell too

OpenStudy (anonymous):

a and b

OpenStudy (anonymous):

you?

OpenStudy (anonymous):

okay (: I've done the Area and Perimeter one, the Derived strings one and The No doubles one.

OpenStudy (kropot72):

The total of the given scores = 12 + 34 + 9 = 55 The smallest possible total weekly score is 3 + 2 + 1 = 6 The factors of 55 are 5 and 11, therefore the number of weeks to achieve the given scores must be 5, the reason being that 5 is too small to be a total weekly score. When the total scores for the additional weeks are added to 55 the new total must have 11 as a factor and must also have 3 as a factor. Can you find the new toal that satisfies all conditions?

OpenStudy (kropot72):

Try 66 as a new total score, since both 3 and 11 are factors. In this case the total score of each of the 3 contestants would be 22. However at the end of week 5 Ben's total score was 34. Therefore the new total must be higher than 66.

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