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
Of course, another (possibly super fast) approach it to check the answer choices.
ADDED BONUS: The total number of wins must be an INTEGER. Since 70% of 156 and 70% of 105 both result in non-integer values for the total number of wins, we need not consider them.
Test answer choice A
Given: the team won 80% of its first 100 games. So, it won
80 games.
If there is a TOTAL of 180 games, then there are
80 games remaining.
The team won 50% of its remaining games. 50% of
80 =
40 wins
80 wins +
40 wins = a TOTAL of
120 wins
Now compare this result with the part about winning 70% of all games.
If there is a TOTAL of 180 wins, then the total number of
wins = 70% of 180 =
156 wins
Doesn't match up - ELIMINATE A
.
.
.
Test answer choice D
Given: the team won 80% of its first 100 games. So, it won
80 games.
If there is a TOTAL of 150 games, then there are
50 games remaining.
The team won 50% of its remaining games. 50% of
50 =
25 wins
80 wins +
25 wins = a TOTAL of
105 wins
Now compare this result with the part about winning 70% of all games.
If there is a TOTAL of 150 wins, then the total number of
wins = 70% of 150 =
105 wins
PERFECT!
Answer:
D
Cheers,
Brent
