Question 834206: I need help figuring out the answer to this word problem.
In a basket ball league, the Falcons won 15% of their first 20 games. In order to win 60% of the total number of games, how many more games will they have to play assuming they win only half of the remaining games?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the number of games they have remaining to play.
then x + 20 must be equal to the total number of games since they already played 20.
your formula becomes:
.15 * 20 + .5 * x = .6 * (x + 20)
.15 * 20 is because you already won 15% of the first 20 games.
.5 * x is because you are assuming that you will win half of the remaining games.
.6 * (x + 20) is because you have to win 60% of the total number of games that you play.
solve this equation and you'll get your answer.
start with:
.15 * 20 + .5 * x = .6 * (x + 20)
simplify to get:
3 + .5 * x = .6 * x + .6 * 20
simplify further to get:
3 + .5 * x = .6 * x + 12
the simplification take into account that .15 * 20 is equal to 3 and .6 * 20 is equal to 12.
you now have the simplified equation of:
3 + .5 * x = .6 * x + 12
subtract 3 from both sides of the equation to get:
.5 * x = .6 * x + 9
subtract .6 * x from both sides of the equation to get:
-.1x = 9
divide both sides of this equation by -.1 to get:
x = -90
you get a negative answer so there's a problem with the equation because it can't be solved the way it's shown.
logicaly it's an impossibility.
50% of the remaining games plus 15% of the first 20 games will never reach 60% of the total games.
assume the problem statement was:
In a basket ball league, the Falcons won 15% of their first 20 games. In order to win 50% of the total number of games, how many more games will they have to play assuming they win only 60% of the remaining games?
now your equation is:
.15 * 20 + .6*x = .5 * (x + 20)
simplify this equation to get:
3 + .6*x = .5*x + 10
subtract 3 from both sides of the equation to get:
.6*x = .5*x + 7
subtract .5*x from both sides of the equation to get:
.1*x = 7
divide both sides of the equation to get:
x = 7 / .1 = 70
this equation is ok because the solution is possible.
you have to win 60% of 70 games plus 15% of 20 games to win 50% of 90 games.
15% of 20 is 3
60% of 70 is 42
total is 45.
50% of 90 is 45.
problem is solved.
your original problem can't be solved because it is impossible to win 60% of the total games if you have won 15% of the first 20 games and only win 50% of the remaining games. In order to make that problem possible, you would have to win more than 60% of the remaining games.
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