Question

Tara bought a bag of 24 large marbles and a bag of 36 small marbles. Tara wants to put the marbles into bags so that there is an equal number of the same size of marbles in each bag and so that there are no marbles left over at all. What is the greatest number of bags that Tara can make? How many of each marble size will there be in each bag? In the box, explain your answer using mathematics.

Answer 1

12 bags 2 large marbles and 3small in each bag

Answer 2

To find the greatest number of bags that Tara can make with an equal number of marbles in each bag, we need to find the greatest common divisor (GCD) of 24 and 36. We can use the Euclidean algorithm to do this:

36 = 24 × 1 + 12

24 = 12 × 2 + 0

Therefore, the GCD of 24 and 36 is 12. This means that Tara can make up to 12 bags with an equal number of marbles in each bag.

To find out how many of each marble size will be in each bag, we need to divide the number of marbles by the number of bags. Since we found that Tara can make up to 12 bags, we can divide the number of marbles in each bag by 12:

24 large marbles ÷ 12 bags = 2 large marbles per bag

36 small marbles ÷ 12 bags = 3 small marbles per bag

Therefore, Tara can make up to 12 bags with 2 large marbles and 3 small marbles in each bag.