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, and each box contained the same number of tiles as each of Bruce’s boxes. She also ran out of tile. She had to go back to the store and get five more tiles to finish the job.

Expression for the number of tiles Bruce used : 5x+2

Expression for the number of tiles Felicia used : 5x + 5

Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.

Suppose, instead, that Bruce used 6 full boxes of tiles plus an additional 2 tiles, and Felicia used 5 full boxes of tiles plus an additional 17 tiles.

If they each used the same number of tiles, how many tiles were in each box?