If $j$, $k$, and $l$ are positive with $jk=24$, $jl = 48$, and $kl=18$, find $j+k+l$.
I notice that the product of any two of the variables is a constant, so I wonder if I can find a way to express one variable in terms of another. I try dividing the first equation by the second equation, and I get $\frac{jk}{jl}=\frac{24}{48}=\frac{1}{2}$. This simplifies to $\frac{k}{l}=\frac{1}{2}$, or $k=\frac{l}{2}$. I can substitute this expression for $k$ into the third equation, and I get $\frac{l}{2}\cdot l=18$. This simplifies to $\frac{l^2}{2}=18$, or $l^2=36$. Taking the positive square root, I get $l=6$. Now that I have $l$, I can find $k$ by plugging it into $k=\frac{l}{2}$. I get $k=\frac{6}{2}=3$. Finally, I can find $j$ by plugging $k$ and $l$ into $jk=24$. I get $j\cdot 3=24$, or $j=8$. Now I have all three variables, and I can add them up to get the answer. I get $j+k+l=8+3+6=17$. 