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
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During a certain season, a team won 80 percent of its first 100 games
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BTGModeratorVI
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If we let G = the TOTAL number of games played in the ENTIRE SEASON, then ...BTGModeratorVI wrote: ↑Fri Jul 03, 2020 7:12 amDuring 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
G - 100 = the number of games REMAINING after the first 100 have been played
We can now start with a "word equation":
(# of wins in 1st 100 games) + (# of wins in remaining games) = (# of wins in ENTIRE season)
We get: (80% of 100) + (50% of G-100) = 70% of G
Rewrite as 80 + 0.5(G - 100) = 0.7G
Expand: 80 + 0.5G - 50 = 0.7G
Simplify: 30 = 0.2G
Solve: G = 150
Answer: D
Brent Hanneson - Creator of GMATPrepNow.com
First \(100\) games \(\Longrightarrow\) win \(80\% = 80\)BTGModeratorVI wrote: ↑Fri Jul 03, 2020 7:12 amDuring 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
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
