Bruce retiled his kitchen. Originally, he bought three boxes of tile with the same number of tiles in each. He ran out of tile and had to go back to get three extra boxes of tile. However, he only used two tiles from the last box to finish the job. Felicia also retiled her kitchen. She bought five boxes of tile with the same number of tiles that were in each as Bruce’s boxes. She also ran out of tile. She had to go back to the store and get an extra five tiles to finish the job.
In this activity, you will determine whether Bruce and Felicia used the same number of tiles and whose tiles cover the most area per tile.


Directions and Analysis
Task 1: One-Variable Linear Equations
a. Write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represent the number of tiles in a box.

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b. To determine whether they used the same number of tiles, set the two expressions equal to each other and solve for x. Is there a solution for x? Why or why not? If there is a solution, what is it?

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c. What conclusion can you draw from this?

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d. How could you change the equation from part 3 so it has infinitely many solutions? What would infinitely many solutions mean in terms of the situation?

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e. If the equation were 6x + 2 = 5x + 17, would there be one unique solution? What is it, and what would it mean in terms of the situation?

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