Brain Teasers
Winning Record
Chanelle has won 429 games and lost 431 games of her favorite computer card game.
If she wins 3 out of every 4 games she plays from now on, how many more games must she play to bring her total winning percentage up to 55%?
If she wins 3 out of every 4 games she plays from now on, how many more games must she play to bring her total winning percentage up to 55%?
Hint
Guess and check and keep track of the number of games won, games lost, and total games played. Better still, use a variable to represent the number of extra games Chanelle must play.Answer
Chanelle must play 220 more games. In these 220 games she wins 3 out of every 4 games, bringing her total of games won to 594 out of 1,080 played (or, 55%).Hide Hint Show Hint Hide Answer Show Answer
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Comments
wow, it is not hard enough but takes a while thinking the solution.
here is my solution:
win lose total game
429 431 860
(+3) (+1) (+4)
-------------------------
432 432 864
(+3) (+1) (+4)
-------------------------
435 433 868
et cetera ...
they form an arithmetic sequence..
win sequence is= 429+3n
lose sequence is= 431+n
total game sequence= 860+4n
the equation becomes
429+3n
--------- x100% = 55%
860+4n
(429+3n)x100= 55x(860+4n)
42900+300n= 47300+220n
-4400= -80n
4400=80n
n= 4400/80= 55
so you need to play 4n = 4x55= 220 more games.
here is my solution:
win lose total game
429 431 860
(+3) (+1) (+4)
-------------------------
432 432 864
(+3) (+1) (+4)
-------------------------
435 433 868
et cetera ...
they form an arithmetic sequence..
win sequence is= 429+3n
lose sequence is= 431+n
total game sequence= 860+4n
the equation becomes
429+3n
--------- x100% = 55%
860+4n
(429+3n)x100= 55x(860+4n)
42900+300n= 47300+220n
-4400= -80n
4400=80n
n= 4400/80= 55
so you need to play 4n = 4x55= 220 more games.
The calculations get easier using 11/20 for 55%.
(429 + .75x) / (429 + 431 + x) = .55
429 + .75x = .55*860 + .55x
429 + .75x = 473 + .55x
.2x = 44
x = 220
429 + .75x = .55*860 + .55x
429 + .75x = 473 + .55x
.2x = 44
x = 220
Excellent teaser. If you just think that out of 4x games she wins 3x you go straight to (429 + 3x)/(860+4x) = 11/20
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