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You can put this solution on YOUR website!
let x equal the number of games they have remaining to play.
\n" ); document.write( "then x + 20 must be equal to the total number of games since they already played 20.
\n" ); document.write( "your formula becomes:
\n" ); document.write( ".15 * 20 + .5 * x = .6 * (x + 20)
\n" ); document.write( ".15 * 20 is because you already won 15% of the first 20 games.
\n" ); document.write( ".5 * x is because you are assuming that you will win half of the remaining games.
\n" ); document.write( ".6 * (x + 20) is because you have to win 60% of the total number of games that you play.
\n" ); document.write( "solve this equation and you'll get your answer.
\n" ); document.write( "start with:
\n" ); document.write( ".15 * 20 + .5 * x = .6 * (x + 20)
\n" ); document.write( "simplify to get:
\n" ); document.write( "3 + .5 * x = .6 * x + .6 * 20
\n" ); document.write( "simplify further to get:
\n" ); document.write( "3 + .5 * x = .6 * x + 12
\n" ); document.write( "the simplification take into account that .15 * 20 is equal to 3 and .6 * 20 is equal to 12.
\n" ); document.write( "you now have the simplified equation of:
\n" ); document.write( "3 + .5 * x = .6 * x + 12
\n" ); document.write( "subtract 3 from both sides of the equation to get:
\n" ); document.write( ".5 * x = .6 * x + 9
\n" ); document.write( "subtract .6 * x from both sides of the equation to get:
\n" ); document.write( "-.1x = 9
\n" ); document.write( "divide both sides of this equation by -.1 to get:
\n" ); document.write( "x = -90
\n" ); document.write( "you get a negative answer so there's a problem with the equation because it can't be solved the way it's shown.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "logicaly it's an impossibility.
\n" ); document.write( "50% of the remaining games plus 15% of the first 20 games will never reach 60% of the total games.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "assume the problem statement was:
\n" ); document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "now your equation is:
\n" ); document.write( ".15 * 20 + .6*x = .5 * (x + 20)
\n" ); document.write( "simplify this equation to get:
\n" ); document.write( "3 + .6*x = .5*x + 10
\n" ); document.write( "subtract 3 from both sides of the equation to get:
\n" ); document.write( ".6*x = .5*x + 7
\n" ); document.write( "subtract .5*x from both sides of the equation to get:
\n" ); document.write( ".1*x = 7
\n" ); document.write( "divide both sides of the equation to get:
\n" ); document.write( "x = 7 / .1 = 70\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "this equation is ok because the solution is possible.
\n" ); document.write( "you have to win 60% of 70 games plus 15% of 20 games to win 50% of 90 games.
\n" ); document.write( "15% of 20 is 3
\n" ); document.write( "60% of 70 is 42
\n" ); document.write( "total is 45.
\n" ); document.write( "50% of 90 is 45.
\n" ); document.write( "problem is solved.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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