Challenge Level

$$\begin{align}(5x+3y)+(10y+30)+(3x+20)&=180\\

8x+13y&=130\\

8\times0+13\times10 &=130\\

\uparrow \hspace{18mm}\uparrow\hspace{2mm} &\\

x\hspace {18mm} y\hspace{2mm}&\end{align}$$

but $x$ shouldn't be $0$

$$\begin{align}13\times10&=130\\8\times13+13\times2&=130\\

\uparrow \hspace{18mm}\uparrow \hspace{1mm}&\\

x\hspace {18mm} y\hspace{1mm}&\end{align}$$ So $x+y=13+2=15$

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.