Question 1045910: Penny collects silver dollars. She's not sure how many dollars she has, but she knows it's fewer than 100.
When she puts them in piles of 2, 1 is left over.
When she puts them in piles of 3, 1 is left over.
When she puts them in piles of 4, 1 is left over.
When she put them in piles of 5, none were left over.
How many silver dollars did she have?
Answer by ikleyn(52813)   (Show Source):
You can put this solution on YOUR website! Penny collects silver dollars. She's not sure how many dollars she has, but she knows it's fewer than 100.
When she puts them in piles of 2, 1 is left over.
When she puts them in piles of 3, 1 is left over.
When she puts them in piles of 4, 1 is left over.
When she put them in piles of 5, none were left over.
How many silver dollars did she have?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let N be the number of silver dollars Penny has.
Take one silver dollar away for a moment and consider the number N-1.
Then N-1 is multiple of 2, 3 and 4.
Hence, N-1 is multiple of 12.
It implies that N might be 13, 25, 37, 49, 61, 73, 85, 97, 109, . . .
From the other side, N must be multiple of 5 and it is less than 100.
Of these numbers, only N = 25 and N = 85 suit for these conditions.
Answer. Penny has either 25 or 85 silver dollars.
|
|
|
