Posted by rich on Sunday, August 19, 2012 at 1:07am.
Jonah has a large collection of marbles. He notices that if he borrows 5 marbles from a friend, he can arrange the marbles in rows of 13 each. What is the remainder when he divides his original number of marbles by 13?

math  Reiny, Sunday, August 19, 2012 at 8:07am
Now that he has the extra 5 marbles, his number must be a multiple of 13, that is, it divides evenly by 13
So obviously before he had the 5 his number must have had a remainder of 5 when divided by 13
e.g suppose he originally had 320
when divided by 13 we get 24 rown with 5 marbles left over. So he gets 5 from his friend and now has 325 , which divides by 13 to get 25 rows.

argh  fuzzy math  Reiny, Sunday, August 19, 2012 at 8:14am
let me try this again.
Now that he has the extra 5 marbles, his number must be a multiple of 13, that is, it divides evenly by 13
So obviously before he had the 5 his number must have had a remainder of 135 or 8 when divided by 13
e.g suppose he originally had 320
when divided by 13 we get 24 rown with 8 marbles left over. So he gets 5 from his friend and now has 325 , which divides by 13 to get 25 rows.
325÷13=25 R 0
324÷13 =24 R 12
323÷13=24 R 11
322÷13 = 24 R 10
321÷13 = 24 R 9
320÷13 = 24 R 8
320÷13 = 24 R 7
etc
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