During a certain season, a team won 80 percent of its first

First...................... Remain ................. Total
100 ........................ x ............................ 100+x

Won
80 ............................. \(\frac{50x}{100}\) ...................... \(\frac{70}{100} * (100+x)\)

Equation would be

\(80 + \frac{50x}{100} = 70 + \frac{70x}{100}\)

x = 50

Total games = 100 + 50 = 150

Answer = D

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 = [spoiler]150[/spoiler]

Answer: D

Given: A team won 80 percent of its first 100 games and 50 percent of its remaining games.
Team won 70 percent of its total games
Required: Total number of games played?

Assume that the remaining games = 100x
Total games won = 80 + 50x
This is 70% of the total games played.

0.7*(100x + 100) = 80 + 50x
70x + 70 = 80 +50x
x = 0.5

Hence 100x = 50

Total games played = 100 + 100x = 150 Option D

Note: We used 100x to avoid the usage of unitary method caused by assuming 100

We are first given that a team won 80 percent of its first 100 games. This means 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 first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season

80 + 0.5T – 50 = 0.7T

30 = 0.2T

300 = 2T

150 = T

Answer is D.

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

This question can be orally solved using weighted averages (yet again!)
Of first 100 (w2) games, team won 80% (A2)
Of the remaining games, it won 50% (A1)
Overall the team won 70% (Aavg)

w1/w2 = (A2 – Aavg)/(Aavg – A1) = (80 - 70)/(70 - 50) = 1/2
Hence w1 = 50

Total number of games = 150
You can ofcourse use the scale method too.

First 100 games -> win 80% = 80
Remaining games -> X
Remaining games won-> (50/100)X
Total games 100first + X -> won 70/100 (100+X)
So..

80+(50/100)x= 70/100 (100+x)
80-70 =(70/100)x-(50/100)x
10 = (20/100)x
x=50 (remaining games) --> Total = 100 +50=150 D

Total games= 100+x
Won= 0.80*100= 80
and also won= 0.50*x

80+0.5x=0.70(100+x)
160+x=(7/5)* (100+x)
800+5x=700+7x
x=50

Therefore total number of games played by the team are (100+50=150).

Let the games above 100 be : Y

What we know. 80% won from 100 & 50 % won from Y games.
Final winning average is 70 %

Equation becomes

.8 * 100 + .5 * Y= .7 * ( 100 + Y)

Solve for y , answer is D = 150

What does the equation mean
LHS: 80 % of 100 games Plus 50 % of remaning Y games will tell us how many total games the team won.
RHS: Tells us if we multiply final winning % with Total games, we will find out how many games the team won.

Since LHS & RHS are telling us the same thing, they become equatable.

Regards

Hi All,

The algebra involved in this question can be written out in a couple of different ways. 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)

80 + .5X = .7(100+X)
80 + .5X = 70 + .7X
10 = .2X
50 = X

Total games played = 100 + 50 = 150

Final Answer:
GMAT assassins aren't born, they're made,
Rich

We can treat this problem as a mixture problem and use weighted averages to solve it(VeritasKarishma ). Weighted Average and Mixture Problems on the GMAT

\(\frac{100}{x} = \frac{(70-50)}{(80-70)}\)
x = 50
total games = 150.

by Plugging In Number method:
Option D : 150 *70% = 105 ------------(1)

i) 100 games : 100*80% = 80
ii) more than 100 games = 50 *50% = 25
adding i) and ii) = 80 + 25 = 105 ------------(2)

from (1) and (2) - option D is correct choice

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