5. The numbers $x$ and $y$ satisfy the equations $x(y+2)=100$ and $y(x+2)=60$. What is the value of $x-y$ ?
A 60
B 50
C 40
D 30
E 20
Solution
E The two equations expand to give $x y+2 x=100$ and $x y+2 y=60$. It follows that $(x y+2 x)-(x y+2 y)=100-60$. That is, $2 x-2 y=40$. Hence $2(x-y)=40$ and so $x-y=20$.