# In an art class

• Jul 28th 2013, 08:15 AM
usre123
In an art class
In an art class, there were just enough staplers, rulers, and glue bottles so that every 2 students had to share a stapler, every 3 students had to share a ruler, and every 4 students had to share a glue bottle. If the sum of the staplers, rulers, and glue bottles used by the class was 65, how many students were in the class?

I have no idea how to do this. If i add 2+3+4= 9. So number of students has to be a multiple of 9. But the answer is 60 students. Could anyone point me in the right direction?
Thanks
• Jul 28th 2013, 08:33 AM
ChessTal
Re: In an art class
Quote:

Originally Posted by usre123
In an art class, there were just enough staplers, rulers, and glue bottles so that every 2 students had to share a stapler, every 3 students had to share a ruler, and every 4 students had to share a glue bottle. If the sum of the staplers, rulers, and glue bottles used by the class was 65, how many students were in the class?

Let's call S the number of all the staplers that have been used by the students, R the number of all rulers that have been used by the students, G the number of glue bottles that have been used by the students and X the number of all the students.

Since every 2 students have to share a stapler, then:
1 stapler has to be shared by 2 students, so:
S staplers has to be shared by X students, so:
2S = X

You do the same with R and X and G and X.
You also know that S+R+G=65 so then you can solve it in a straightforward way.

Quote:

I have no idea how to do this. If i add 2+3+4= 9. So number of students has to be a multiple of 9.
Why exactly?
• Jul 28th 2013, 09:57 AM
usre123
Re: In an art class
Thanks ChessTal, your on a roll:-)
I thought that when we're told, for example, the ratio of peaches to apples is 2:3, then the total number of peaches and apples has to be a multiple of 5. But I realize the mistake I made: I wasn't given student ratios to begin with.