Question

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 number of staplers, rulers, and glue bottles used by the class was $65$ , how many students were in the class?

Answer 1

Given 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.

let the number of staplers,rulers,glue bottles be $a,b,c$ respectively.

Given $a+b+c=65$.

Let the number of students be $n$, we get $n=2a,n=3b,n=4c$

Therefore $\frac{n}{2}+\frac{n}{3}+\frac{n}{4}=65$ , which implies $\frac{13n}{12}=65$.

So we get $n=60$