Posted by **jill** on Tuesday, October 20, 2009 at 5:14pm.

Between 50 and 100 grade 7 students at school are having a bbq. Each student will receive one hot dog. Hot dogs come in packages of 12 and buns in packages of 8. How many students are in grade 7, if all the packages of hot dogs and buns purchased are used up?

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**Ms. Sue**, Tuesday, October 20, 2009 at 5:19pm
It could be 72 or it could be 96.

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**jill**, Tuesday, October 20, 2009 at 5:57pm
how could it be 72 or 96, I am confused

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**jim**, Tuesday, October 20, 2009 at 6:01pm
Whatever number it is has to divide evenly both by 12 and by 8.

For example, could it be 80?

Well, that would use up exactly 10 packages of 8 buns, but would it use up exactly some number of packages of hot dogs?

So it can't be 80. And similarly, it can't be 50, or 81, or 95, or... because there would not be an even number of packages used for one or the other.

Now try the numbers Ms. Sue gave!

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**Reiny**, Tuesday, October 20, 2009 at 6:06pm
The lowest common multiple of 12 and 8 is 24

after that would come

48 72 96 120 ..

Now which lie between 50 and 100, the number of students ?

Ms. Sue is right.

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