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# A professional gambler has won 40% of his 25 poker games for

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A professional gambler has won 40% of his 25 poker games for [#permalink]  28 Sep 2007, 04:23
A professional gambler has won 40% of his 25 poker games for the week so far. If all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?

I'm little confused by this question. The first part says he played 25 games for the week and he won 40% so he won 10 games. I don't understand the second line and how it will fit to give me an answer. When it says 80% of time, what does that mean? What does that 80% of time relate to next week, next two weeks, next month ??????

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for the week so far

the week has not ended yet
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40% means that for every 2 games he wins he lose 3.
80% means that for every 4 games he wins he lose 1.

after 25 games at 40% ---> won 10 and lost 15

after x more games at 80% ---> won (x/5)*4 and lost x/5

so in order to get 60% total winning:

(10+(x/5)*4)/(25+x) = 3/5

(10+4x/5)/(25+x) = 3/5

5*(10+4x/5) = 75+x

50+4x = 75+x

x = 25

x = 50 ---> he has to play 50 games.

first 25 games ---> win 10 lose 15 ---> 10/25 = 40%
then 25 games ---> win 20 lose 5 ---> 20/25 = 80%

total 50 games ---> win 30 lose 20 ---> 30/50 = 60%

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Thanks killersquirrel and ronron.. Now I got it.
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