Question

2. Mark has scored 12, 14, 10, 8, and 5 points in the past 5 basketball games. Write and solve the inequality that

Answer 1

Answer:

  Mark must score at least 11 points to have an average of 10 points per game.

Step-by-step explanation:

The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 10, then the relation is ...

  (12 +14 +10 +8 +5 +p)/6 ≥ 10

  49 +p ≥ 60 . . . . . . . . . multiply by 6 and simplify

  p ≥ 11 . . . . . . . . . . . subtract 49

Mark must score at least 11 points in the next game to average at least 10 points per game.

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Additional comment

Sometimes, it is convenient to work with the average directly. Relative to the average Mark wants (10), his scores so far are +2, +4, 0, -2, -5, for a total of -1. In order to bring the average to the value Mark wants, he must bring this total to 0 or higher. That is, he must score at least 10+1 = 11 points in his next game.