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?

• A. $180$
• B. $170$
• C. $156$
• D. $150$
• E. $105$

Answer 1

Answer: (D)

$150$

$\Rightarrow$ We are first given that a team won $80\%$ of its fist 100 games.

$\Rightarrow$ This means team won $\frac{80}{100}\times 100=80$ games out of its 100 games.

$\Rightarrow$ Next given that the team won $50\%$ of its remaining games.

$\Rightarrow$ Let $x$ be the total number of games in season, then we can say $x-100$ equals the number of remaining games in the season.

$\Rightarrow$ So, Number of wins for remaining games = $50\%(x-100)=0.5x-50$

$\Rightarrow$ Lastly, We are given that team won $70\%$ of all games played in the season. Which means they won $0.7x$ games in the entire season. With this we can form equation:

$\Rightarrow$ Total number of games won in the entire season = Number of first 100 games won + Number of games won for remaining games

$\Rightarrow$ $0.7x=80+0.5x-50$

$\Rightarrow$ $0.2x=30$

$\Rightarrow$ $2x=300$

$\therefore$ $x=150$