Question

In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60
B) 70
C) 80
D) 90
E) 100

Answer 1

By establishing the total number of games played in the first half of the year as G, and using the information provided about the win percentages for each half of the year, we can set up the equation 0.5(G + 20) = 0.6G + 3 and solve for G, resulting in the total number of games played being 70.

Step-by-step explanation:

We need to solve for the total number of games played last year by the team. We know the team won 50 percent of its games over the entire year, and we also have information about the number of games won in each half of the year.

• Let G represent the total number of games played in the first half of the year.
• The team won 60 percent of these games, so they won 0.6G games.
• In the second half of the year, the team won 3 out of 20 games played.
• Combining both halves of the year, the team won 0.6G + 3 games.
• Since they won 50% of games over the entire year, the equation 0.5(G + 20) = 0.6G + 3 can be formed.
• Solving for G, we find that G = 50 games.
• Total games played over the year = G + 20 (second half games) = 50 + 20 = 70 games (Answer B).

Answer 2

By setting up an equation with the information provided, it is determined that the team played a total of 90 games last year, making the correct answer option D) 90.

Step-by-step explanation:

To solve this problem, let's denote the total number of games played in the first half of the year as x. According to the question, the team won 60 percent of these games. Therefore, the team won 0.6x games in the first half of the year. In the second half of the year, the team played 20 games and won 3 of them.

The question also tells us that the team won 50 percent of all the games played throughout the year. The total number of games played in the year is therefore x (from the first half) + 20 (from the second half). The total number of wins is 0.6x (from the first half) + 3 (from the second half).

To find the total number of games played last year, we need to set up an equation where the total wins (0.6x + 3) constitute 50 percent of the total games (x + 20):

0.6x + 3 = 0.5(x + 20)

Solving for x gives:

0.6x + 3 = 0.5x + 10

0.1x = 7

x = 70

Therefore, the total number of games played last year is x + 20, which is 70 + 20 = 90 games.

The correct answer is D) 90.