Question

use the information to answer the following question.
a student is playing a game where, on each turn, he can score either 3 or 6 points. he is allowed to take no more than 10 turns
scores at least 39 points.
let x represent the number of turns in which he scores 6 points, and y represent the number of turns in which he scores 3 poin
he considers choosing 2 6 - point turns and 8 3 - point turns.
which statement best justifies whether this is a winning strategy?
a this is a winning strategy because he does score enough points.
b this is not a winning strategy because he will take more than 10 turns.
c this is not a winning strategy because he does not score enough points.
d this is a winning strategy because he does not exceed 10 turns.

Explanation:

Step1: Calculate total turns

The number of 6 - point turns is \(x = 2\) and the number of 3 - point turns is \(y=8\). The total number of turns is \(x + y=2 + 8=10\) turns, which is within the limit of no more than 10 turns.

Step2: Calculate total points

The total points scored is calculated by the formula \(6x+3y\). Substitute \(x = 2\) and \(y = 8\) into the formula: \(6\times2+3\times8=12 + 24=36\) points.
Since the requirement is to score at least 39 points and \(36<39\), the student does not score enough points. Also, the total number of turns is \(10\) which is not more than 10. So the reason is that he does not score enough points.

Answer:

C. This is not a winning strategy because he does not score enough points.