SOLUTION: I have tried this problem 3 times and have came up with 3 different answers. Can you please help me? Paige has won 429 games and lost 431 games of her favorite card game. If she w

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: I have tried this problem 3 times and have came up with 3 different answers. Can you please help me? Paige has won 429 games and lost 431 games of her favorite card game. If she w      Log On


   

Question 132990: I have tried this problem 3 times and have came up with 3 different answers. Can you please help me? Paige has won 429 games and lost 431 games of her favorite card game. If she wins 3 out of every 4 games she play from now on, how many more games must she play to bring her total winning percentage up to 55%?
Found 2 solutions by checkley71, nycsharkman:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
(429+3X)/(429+431+4X)=.55 .
(429+3X)/(860+4X)=.55 NOW CROSS MULTIPLY
.55(860+4X)=429+3X
473+2.2X=429+3X
2.2X-3X=429-473
-.8X=-44
X=-44/-.8
X=55 ADDITIONAL GAMES WILL BE REQUIRED.
PROOF:
(429+3*55)/(860+4*55)=.55
(429+165)/(860+220)=.55
594/1080=.55
.55=.55

Answer by nycsharkman(136) About Me  (Show Source):
You can put this solution on YOUR website!
Let us assume that she has to play 4x games
to make the winning percentage of 55%
Out of the 4x games played,she is supposed to win 3x games
(429+3x)/(429+431+4x)=55/100
(429+3x)/(860+4x)=11/20
8580+60x=9460+44x
60x-44x=9460-8580
16x=880
x=880/16=55
Therefore,she should play 4 x 55 or 220 more games.