Question

During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

Answer 1

Answer: 150

Step-by-step explanation:

Let x be the  total number of games that the team played.

Given : During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games.

No. of games won out of first 100 games =0.80(100)               (1)

Remaining games = x-100

No. of games won out of remaining games=0.50(x-100)                   (2)

If the team won 70 percent of its games for the entire season ,

Number of games won by team = 0.70x

Then According to the given question , we have

No. of games won by team= No. of games won out of first 100 games + No. of games won out of remaining games

$0.80(100)+0.50(x-100)=0.70x\ \ \\\\\Rightarrow\ 80+0.5x-50=0.7x\\\\\Rightarrow\ 0.7x-0.5x=30\\\\\Rightarrow\ 0.2x=30\\\\\Rightarrow\ x=\dfrac{30}{0.2}=150$

Hence, the total number of games that the team played= 150