LCM question -- how many packages of burgers and cheese slices to buy?

[paulb203]

Homework Statement

Q. Rita is going to make some cheeseburgers for a party.
She buys some packets of cheese slices and some boxes of burgers.
There are 20 cheese slices in each packet.
There are 12 burgers in each box.
Rita buys exactly the same number of cheese slices and burgers.
How many packets of each does she buy?

Relevant Equations

N/A

My attempt at an answer. I’m pretty sure this is an LCM question (Lowest Common Multiple).

I started listing the prime factors for the cheese slices; 20 = 2^2 x 5

Then the burgers; 12 = 2^2 x 3

Then put the factors in a Venn diagram and found the LCM was 60

Then divided 60 by 20 for the cheese slices = 3 packets

Then divided 60 by 12 for the burgers = 5 boxes

 

[phinds]

Correct, and your question is?

 

[FactChecker]

If you are in doubt about your work and final answer, you should always go back to the original problem statement and check if you answer works. It does.

 

[Ibix]

Incidentally, the problem as stated is ambiguous. 120, or 180, or 240, or any integer multiple of 60 will also work. Hopefully the original problem statement also says something like "the smallest number of packets she can buy", or "she knows she won't need more than 100" or something.

 

[WWGD]

Incidentally, the problem as stated is ambiguous. 120, or 180, or 240, or any integer multiple of 60 will also work. Hopefully the original problem statement also says something like "the smallest number of packets she can buy", or "she knows she won't need more than 100" or something.

Anything above 60 send by express mail to the PF lounge.

 

[paulb203]

Correct, and your question is?

Thanks, phinds.
My question is; is it correct? What about 6 packets and 10 boxes. Or 12 packets and 20 boxes. Etc, etc?

Q. Is the question badly worded?

 

[paulb203]

If you are in doubt about your work and final answer, you should always go back to the original problem statement and check if you answer works. It does.

Thanks, FactChecker.
I did go back and check, but I'm wondering if my answer is correct or not. Could it not have been more packets and boxes?

 

[paulb203]

Incidentally, the problem as stated is ambiguous. 120, or 180, or 240, or any integer multiple of 60 will also work. Hopefully the original problem statement also says something like "the smallest number of packets she can buy", or "she knows she won't need more than 100" or something.

Thanks, Ibix. That's what I was wondering. As for the original problem statement; I've quoted it word for word.

 

[FactChecker]

Thanks, FactChecker.
I did go back and check, but I'm wondering if my answer is correct or not. Could it not have been more packets and boxes?

Yes. Any common multiple would literally answer that question. But they probably wanted you to give the least common multiple as you did.

 

[Steve4Physics]

Surely two slices of cheese per burger: e.g here.

 

[DaveC426913]

Incidentally, the problem as stated is ambiguous.

Not if you include the title of the thread, which states it is a LCM question. Is the chapter of the book called LCM?

 

[DaveC426913]

Apropos of nothing.

Mark my words, the day will come when food product companies learn about prime numbers and start producing packages of 13 patties, 17 buns and 19 cheese slices. (Now the question becomes how many party-goers do you need to invite (or hire) to get all the burgers eaten.)

 

[paulb203]

Not if you include the title of the thread, which states it is a LCM question. Is the chapter of the book called LCM?

Ah, that wasn't part of the question.

 

[paulb203]

Apropos of nothing.

Mark my words, the day will come when food product companies learn about prime numbers and start producing packages of 13 patties, 17 buns and 19 cheese slices. (Now the question becomes how many party-goers do you need to invite (or hire) to get all the burgers eaten.)

One of my favourite philosophers, Apropos of Nothing. Up there with Zeno of Elea.