Mrs. Graham is creating student envelopes for a math activity in her class. She has 64 problems written on pieces of blue paper and 48 problems written on pieces of red paper. She needs to sort the pieces of paper so that each envelope has the same number of pieces and no envelope has both red and blue pieces.
If Mrs. Graham puts the greatest possible number of papers in each envelope, how many papers will go in each envelope?
How many envelopes can Mrs. Graham create if she puts the greatest possible number of papers in each envelope? (( medal for who answers and fan )) :))

Question

Mrs. Graham is creating student envelopes for a math activity in her class. She has 64 problems written on pieces of blue paper and 48 problems written on pieces of red paper. She needs to sort the pieces of paper so that each envelope has the same number of pieces and no envelope has both red and blue pieces.
If Mrs. Graham puts the greatest possible number of papers in each envelope, how many papers will go in each envelope?
How many envelopes can Mrs. Graham create if she puts the greatest possible number of papers in each envelope? (( medal for who answers and fan )) :))

ganeshie8 · Answer

|dw:1405558731891:dw|

ganeshie8 · Answer

lets be greedy,
put try to put 48 papers in each envelope

ganeshie8 · Answer

we can NOT do that cuz 48 doesn't go evenly into 64, 
so there will be a remainder for the blue papers

ganeshie8 · Answer

$\large \color{red}{64} = \color{red}{48}(1) +  16$

ganeshie8 · Answer

lets see if we can 16 papers in each envelope :

$\large \color{red}{48} = \color{red}{16}(3) +  0$

Oh yes ! so gcf of 64 and 48 is 16
so the maximum number of papers that you can put in each envelope is $16$

ganeshie8 · Answer

if that makes any sense..

anonymous · Answer

definitely thanks :)

ganeshie8 · Answer

|dw:1405559193472:dw|