If $a\times b=2$, $b\times c=24$, $c\times a=3$ and $a$, $b$ and $c$ are all positive, what is the value of $a+b+c$?

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This problem is taken from the UKMT Mathematical Challenges.

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Expanding and factorising quadratics. Simultaneous equations. Generalising. Mathematical reasoning & proof. Polynomial functions and their roots. Regular polygons and circles. Inequalities. 2D shapes and their properties. Working systematically. Circle properties and circle theorems. Creating and manipulating expressions and formulae.