Final answer:
Ben must score at least 177 in his third game to have an average of 180 over three games. Since this value is below all the options provided, the correct answer is option B. 192, which is the lowest choice that is more than 177.
Step-by-step explanation:
To determine what Ben must bowl in his third game to have an average of at least 180, we start by calculating the total number of points he needs over the three games. To have an average of 180, Ben must have a total of 180 × 3, since average is the total sum divided by the number of games, which is 540 points. So far, Ben has scored 149 in his first game and 214 in his second game, which adds up to 363 points. To find out what he needs to score in the third game, we subtract the total points he has from the desired total point threshold.
The calculation would be as follows:
- Calculate desired total points: 180 × 3 = 540 points.
- Add Ben's first two game scores: 149 + 214 = 363 points.
- Subtract the sum of the first two games from the desired total: 540 - 363 = 177 points.
Therefore, in order to have an average of at least 180 after three games, Ben must score at least 177 in his third game. To answer the multiple-choice question, he must score 177 or higher, which means the correct answer is option B. 192, as it is the smallest option more than 177.