Problema Solution
Cindy works with the school store. She has 24 pencils and 36 pens. How many bags of pencils and pens can she full if she puts the same number of pencils and the same number of pens in each bag and uses them all? Find all the possibilities. Explain your reasoning.
Answer provided by our tutors
The common factors of 24 and 36 are: 1, 2, 4, 6, 12 (since 24 = (2^3)*3 and 36 = (2^2)*(3^2)).
Since she needs to put same number of pencils and same number of pens in each bag we are using the common factor as the number of bags needed:
She can use 1 bag at put all of them in it.
She can use 2 bags and put: 24:2 = 12 pencils and 36:2 = 18 pens in each.
She can use 4 bags and put: 24:4 = 6 pencils and 36:4 = 9 pens in each.
She can use 6 bags and put: 24:6 = 4 pencils and 36:6 = 6 pens in each.
She can use 12 bags and put: 24:12 = 2 pencils and 36:12 = 3 pens in each.