## 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*} place four times of the 2012 season, and won \begin{align*}2^{nd}\end{align*} place three times. With these wins on the MotoGP website, he earned a total of 160 points so far. But what does this mean? How can we figure out how many points are awarded to \begin{align*}1^{st}\end{align*} place and how many points are awarded to \begin{align*}2^{nd}\end{align*} place?

We can represent this as an expression (and, if you’re daring, as an equation). We can let \begin{align*}x\end{align*} represent the number of points awarded for \begin{align*}1^{st}\end{align*} place, and \begin{align*}y\end{align*} represent the number of points awarded for \begin{align*}2^{nd}\end{align*} place. How many possibilities can we plug in for \begin{align*}x\end{align*} and \begin{align*}y\end{align*} so that the total number of points equals 160? Obviously, the number of points awarded for first place has to be higher than the number of points for \begin{align*}2^{nd}\end{align*} place.

If the number of points awarded for \begin{align*}1^{st}\end{align*} place were 20 points per race, how many points are awarded for \begin{align*}2^{nd}\end{align*} place? Let’s figure this out using expressions.

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

Now, what values can we substitute for \begin{align*}y\end{align*} so that the total number of points is 160?

If we substituted 26 in for \begin{align*}y\end{align*}, the total number of points would be too low. \begin{align*}80 + 3(26) = 80 + 78 = 158\end{align*}.

If we substituted 27 in for \begin{align*}y\end{align*}, the total number of points would be too high. \begin{align*}80 + 3(27) = 80 + 81 = 161.\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*} place was awarded 25 points per game? If this were true, how many points would second place be?

\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