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Question

All the pupils in the Mathematics Club were each given a box of jelly beans on Children's Day. The girls received 923 jelly beans altogether and the boys received 1157 jelly beans altogether. Hoe many pupils are there in the Mathematics Club altogether. (Assume that there are the same number of jelly beans in each box.)

Answer 1

There are N jelly beans in each box, X boys and Y girls.

 

Then the total number of jelly beans the girls received is NY, the total number the boys received is NX.  Since N, X and Y are integers, you need do prime factorization of 923 and 1157.

 

sqrt(923) = 30.38, so one of the factors of 923 is less than 30.  It can't be even, it can't end in 5, that leaves:

 

3,7,9,11,13, 17, 19, 23, 29 (other numbers are not prime)

 

Quick use of a calculator shows that 923 is divisible by 13.  923 = 13*71

 

Then N is either 13 or 71.  Again, using a calculator shows that 1157/13 = 89, and 1157/71 is not an integer.

 

So: 923 = 13*71

1157 = 13*89

 

That means N=13,  X = number of boys = 89, Y = number of girls = 71, and the total number of pupils is:

89 + 71 = 160