Problem Solving

The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?

A. 6
B. 7
C. 8
D. 9
E. 10

The OA is C.

I'm confused by this PS question. Experts, any suggestion about how can I solve it? Thanks!

LUANDATO wrote:The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?

A. 6
B. 7
C. 8
D. 9
E. 10

Since 9 points have been earned after 5 games, the team must earn 31 more points over the next 15 games to reach the 40-point mark.
We can PLUG IN THE ANSWERS, which represent the least number of games that must be won.
To MINIMIZE the number of wins, we must MAXIMIZE the number of points earned for each game that is NOT won.
Implication:
Every game that is not won must end in a DRAW, so that the team earns a point for each game that is not won.
Since we are asked for the least number of games that must be won, start with the smallest answer choice.
When the correct answer is plugged in, the team will earn at least 31 more points over the remaining 15 games.

A: 6 games are won, 9 games end in a draw
Since 3 points are earned for each win, and 1 point is earned for each draw, we get:
Total points earned = (6*3) + (9*1) = 27.
Since the team must earn at least 31 more points, eliminate A.

B: 7 games are won, 8 games end in a draw
Since 3 points are earned for each win, and 1 point is earned for each draw, we get:
Total points earned = (7*3) + (8*1) = 29.
Since the team must earn at least 31 more points, eliminate B.

C: 8 games are won, 7 games end in a draw
Since 3 points are earned for each win, and 1 point is earned for each draw, we get:
Total points earned = (8*3) + (7*1) = 31.
Success!

The correct answer is C.