<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.
You are viewing an older version of this Concept. Go to the latest version.

Expressions with One or More Variables

Evaluate expressions given values for variables.

Atoms Practice
Estimated15 minsto complete
%
Progress
Practice Expressions with One or More Variables
Practice
Progress
Estimated15 minsto complete
%
Practice Now
MotoGP
teacher Contributed

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 send 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

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Expressions with One or More Variables.
Please wait...
Please wait...