Problem Solving

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

If we let G = the TOTAL number of games played in the ENTIRE SEASON, then ...
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

Hi Beth,

The algebra involved in this question can be written out in a couple of different ways. Here's a slightly different variation:

We're told that a team won 80% of its first 100 games and 50% of the remaining games

Initial wins = .8(100) = 80
Later wins = .5(X) = .5X

Total wins = 80 + .5X
Total games played: (100+X)

We're also told that the team won 70% of the games that it played for the ENTIRE SEASON. We now how 2 different pieces of information that mean the same thing, so we can set them equal to one another....

Total wins = .7(100+X)

Total wins = 80 + .5X = .7(100+X)

From here, we have a 1 variable and 1 equation, so we CAN solve for X.

GMAT assassins aren't born, they're made,
Rich

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

[email protected] wrote: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?

G= games

(.80)(100) +.50(G-100)= .70G


I don't understand how the second 100 is included in the equation. Can I have an experts help?

Thank-you!
Beth

Solution:

We are first given that a team won 80 percent of its first 100 games. Thus, the team won 0.8 x 100 = 80 games out of its first 100 games.

We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say (T - 100) equals the number of remaining games in the season. Thus, we can say:

0.5(T - 100) = number of wins for remaining games

0.5T - 50 = number of wins for remaining games

Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:

Number of games won from first 100 games + Number of games won from the remaining games = Total Number of games won in the entire season

80 + (0.5T - 50) = 0.7T

30 + 0.5 T = 0.7T

30 = 0.2T

300 = 2T

150 = T

Answer: D