Packs of pencils required in equal

Question

Stuck on the below question with my $9$-year old - any ideas on this one?

Really don't know how to even start on this one..I know half of $72$ is $36$ but not too sure how that will help here...any assistance would be good..

Pencils come in packages of $36$ and rubbers come in packages of $72$. Judith wants to divide them so that each group has equal number of pencils and rubbers. How many packages of pencils does she need to buy to have the smallest number of pencils?

Answer 1

I think the question is very badly worded, as it's not really clear what it means by "each group has..". With the way it's worded, it implies that you have to share out the pens and pencils equally among an unspecified number of groups. Without knowing the number of groups, this makes the question unsolvable: for example, if you had $3$ groups, then you'd need to buy $2$ packs of pencils and $1$ of rubbers. But if there were $16$ groups, then you'd need $4$ packs of pencils and $2$ of rubbers.

It seems that what the question is trying to ask is:

Judith wants to buy a certain number of packs of pencils and rubbers so that she has the same amount of each.

In which case, the answer is as the teacher has said. But this is far from clear.

Answer 2

I've seen a lot of similar questions, helping my kid with math, and I am almost certain that this question is missing information about how many groups there are, as that would have been a very common math question for an elementary school student.

Usually, in these types of questions, it's not so much about that they get the same amount of pencils and rubbers, but that each group get the same, so if there had been 18 groups, 1 pack of each would give each group 2 pencils and 4 rubbers.