Cy has 42 baseball cards and 70 football cards that he wants to group into packages. each package will have the same number of cards. how many packages will cy make if he uses all of the cards

Cy has 42 baseball cards and 70 football cards

he wants to group them into packages with each package having the same number of cards of both types

so we have to find the highest common factor for 42 and 70 so they can be divided into packages equally and each package having an equal number of cards

the factors for 42 and 70 are as follows

42 - 1,2,3,6,7,14,21,42

70 - 1,2,5,7,10,14,35,70

the highest factor common for both is 14

therefore Cy can make 14 packages

each package will have

42/14 = 3 baseball cards

70/14 = 5 football cards

so each package will have 3 baseball cards and 5 football cards

Cy can make 14 packages

If Cy uses all the cards, then there will be 3 baseball cards and 5 football cards in each pack, that is - assuming that each pack needs to have each type of card within it. Overall then, there will be 14 different packages built from his overall collection of cards.