The point P(7, 1) divides the segment joining A(k, 10) and B(9, -2) in the ratio 3 : 1.
Find the value of k.

Using the $x$-coordinate: $\frac{3\cdot 9+1\cdot k}{3+1}=7$, so $27+k=28$ and $k=1$. Check with $y:\frac{3\cdot (-2)+1\cdot 10}{4}=\frac{4}{4}=1$. The value 5 treats P as the midpoint and solves $\frac{k+9}{2}=7$; -6 divides by $m=3$ instead of by $m+n=4$; 28 clears the denominator but then forgets to subtract 27.