## Real World Applications – Algebra I

### Topic

How are points accumulated in MotoGP?

### Student Exploration

MotoGP is the top class of the World Championship Grand Prix for motorcycle road racing. For this class, one of the favorite riders is Jorge Lorenzo. By July 2012, he had won \begin{align*}1^{st}\end{align*}

We can represent this as an expression (and, if you’re daring, as an equation). We can let \begin{align*}x\end{align*}

If the number of points awarded for \begin{align*}1^{st}\end{align*}

\begin{align*}& 4x + 3y\\
& 4(20) + 3y\\
& 80 + 3y\end{align*}

Now, what values can we substitute for \begin{align*}y\end{align*}

If we substituted 26 in for \begin{align*}y\end{align*}

If we substituted 27 in for \begin{align*}y\end{align*}

Typically, points in races are awarded as whole numbers. So, first place must not be worth 20 points.

What if \begin{align*}1^{st}\end{align*}

\begin{align*}& 4(25) + 3y\\
& 100 + 3y\end{align*}

Now, what value of \begin{align*}y\end{align*} can we substitute so that the number of points would equal 160?

\begin{align*}& 100 + 3(20)\\ & 100 + 60\\ & 160\end{align*}

By evaluating expessions, we were to find out how many points were awarded to both \begin{align*}1^{st}\end{align*} and \begin{align*}2^{nd}\end{align*} place winners for MotoGP races. You can even check your answer here: http://www.motogp.com/en/MotoGP+Basics/points

### Extension Investigation

Try researching another sporting event and find out how points are awarded for each game. It’s different for every sport! Using a similar method that we used here for this investigation, how can you use expressions to figure out how many points are awarded to a specific player if you only have the total number of wins and the total number of points?

### Resources Cited

www.motogp.com