BTGModeratorVI wrote: ↑

Fri Jul 03, 2020 7:12 am

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: D
Source: Official guide

First \(100\) games \(\Longrightarrow\) win \(80\% = 80\)
Remaining games \(\Longrightarrow X\)
Remaining games won \(\Longrightarrow (50/100)X\)
Total games \(100\) first \(+ X \Longrightarrow\) won \(\dfrac{70}{100} (100+X)\)
So.

\(80+\dfrac{50}{100}x= \dfrac{70}{100} (100+x)\)
\(80-70 ={70}{100}x-\dfrac{50}{100}x\)
\(10 = \dfrac{20}{100}x\)

\(x=50\) (remaining games) \(\Longrightarrow\) Total \(= 100 +50=150 \Longrightarrow\) D