Tamika enjoys playing chess and Scrabble. Every chess game takes exactly 45 minutes and each game of Scrabble takes exactly 30 minutes. For all parts of the problem, Tamika wants to play at least 10 total games, but she only has at most six hours available.

  1. Write an inequality that represents the minimum number of games Tamika wants to play. (2 pts)
  2. Write an inequality that represents the number of games she can play in her time limit. (2 pts)
  3. Graph these two inequalities on the same coordinate system. (3 pts)
  4. If Tamika wants to play as many total games as possible, what combination of games should she play? Is there more than one way to play this number of games? (3 pts)
  5. If Tamika wants to play the most number of chess games as possible while still playing at least ten total games in the six hours she has, how many games of chess could she play? (3 pts)
  6. If Tamika wants to play exactly ten games, what combinations of Scrabble and chess could she play in the six hours available? If there is more than one combination, please list them all. (3 pts)

Remember, complete English sentences should be written explaining what you are doing at each step as well as a justification of that process. There should be at least as much writing on your submission as there is math!

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