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# Expressions with One or More Variables

## Evaluate expressions given values for variables.

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Practice Expressions with One or More Variables
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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 1st\begin{align*}1^{st}\end{align*} place four times of the 2012 season, and won 2nd\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 1st\begin{align*}1^{st}\end{align*} place and how many points are awarded to 2nd\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 x\begin{align*}x\end{align*} represent the number of points awarded for 1st\begin{align*}1^{st}\end{align*} place, and y\begin{align*}y\end{align*} represent the number of points awarded for 2nd\begin{align*}2^{nd}\end{align*} place. How many possibilities can we plug in for x\begin{align*}x\end{align*} and y\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 2nd\begin{align*}2^{nd}\end{align*} place.

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

4x+3y4(20)+3y80+3y

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

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

If we substituted 27 in for y\begin{align*}y\end{align*}, the total number of points would be too high. 80+3(27)=80+81=161.\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 1st\begin{align*}1^{st}\end{align*} place was awarded 25 points per game? If this were true, how many points would send place be?

4(25)+3y100+3y

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

100+3(20)100+60160

By evaluating expessions, we were to find out how many points were awarded to both 1st\begin{align*}1^{st}\end{align*} and 2nd\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?

www.motogp.com