Posted by rich on .
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,
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,
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