Question

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

can be used to solve for the number of points he will need to score in the next game in order for Mark to
average at least 10 points per game.
Be sure to define your variable. You must also write one sentence to explain what your answer means in the
context of the problem,

Answer 1

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

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.

_____

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.