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Math Help - In an art class

  1. #1
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    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?

    No choices, we had to give our own answer.

    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
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  2. #2
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    Re: In an art class

    Quote Originally Posted by usre123 View Post
    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?

    No choices, we had to give our own answer.
    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.


    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?
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  3. #3
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    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.
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