ILL 1982 Problem 6

On the three distinct lines $a, b$ , and $c$ three points $A, B$ , and $C$ are given, respectively. Construct three collinear points $X, Y,Z$ on lines $a, b, c$ , respectively, such that $\frac{BY}{AX} = 2$ and $\frac{CZ}{AX} = 3$ .