Problema Solution
Will was counting the new state quarters that he had been collecting. He started organizing them into piles. He put all of the quarters into piles of three but found that there were two left over. Then he put them into piles of five and found that there were three left over. Then he put them into piles of seven and found that there were five left over. Finally, he put them into piles of two, and there weren’t any left over. Will has fewer than 100 quarters. How many quarters does he have?
Answer provided by our tutors
The possible solutions are multiple of 7 plus 5:
7 + 5 = 12
2*7 + 5 = 19
3*7 + 5 = 26
4*7 + 5 = 33
5*7 + 5 = 40
6*7 + 5 = 47
7*7 + 5 = 54
7*8 + 5 = 61
7*9 + 5 = 68
7*10 + 5 = 75
7*11 + 5 = 82
7*12 + 5 = 89
7*13 + 5 = 96
Using the fact that if he puts them into 2 piles there are no leftovers we conclude that the number of quarters my be event number, thus we eliminate the odd number from above and we are left with the following possibilities:
12
26
40
54
68
82
96
When he puts them in a pile of 5 there are 3 left.
12 = 5*2 + 2 follows this is not the answer
26 = 5*5 + 1 follows this is not the answer
40 = 5*8 follows this is not the answer
54 = 5*10 + 4 follows this is not the answer
68 = 5*13 + 3 - possible answer
82 = 5*16 + 2 follows this is not the answer
96 = 5*19 + 1 follows this is not the answer
When put into piles of 7 there are 5 left over:
68 = 9*7 + 5
The answer is: Will has 68 quarters.