## Task

Chase and his brother like to play basketball. About a month ago they decided to keep track of how many games they have each won. As of today, Chase has won 18 out of the 30 games against his brother.

- How many games would Chase have to win in a row in order to have a 75% wining record?
- How many games would Chase have to win in a row in order to have a 90% winning record?
- Is Chase able to reach a 100% winning record? Explain why or why not.
- Suppose that after reaching a winning record of 90% in part (b), Chase had a losing streak. How many games in a row would Chase have to lose in order to drop down to a winning record below 55% again?

## IM Commentary

This task provides a simple but interesting and realistic context in which students are led to set up a rational equation (and a rational inequality) in one variable, and then solve that equation/inequality for an unknown variable. It seems likely to be direct and relevant enough to be used for assessment purposes, either in part or in whole. Alternatively, this task could be used as a motivation for studying equations of this form in general, as while students might be able to solve the first part by trial and error, this becomes rather tedious for the later parts. Teachers might also find this task could be used to illustrate standard A-REI.A.1 if some more emphasis were placed on the reasoning behind the algebraic manipulations provided in the solutions.