document.write( "Question 1044759: A violinist is learning a waltz and a sonatina. One day she practices for 33 minuts by playing the waltz 4 times amd the sonatina 3 times. The next day she plays the waltz 6 times and the sonatina only once, for the total of 25 minutes. Using algebraic method, determine the length of each piece. \n" ); document.write( "

Algebra.Com's Answer #660137 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A violinist is learning a waltz and a sonatina. One day she practices for 33 minutes by playing the waltz 4 times and the sonatina 3 times.
\n" ); document.write( "The next day she plays the waltz 6 times and the sonatina only once, for the total of 25 minutes. Using algebraic method,
\n" ); document.write( "determine the length of each piece.
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document.write( "Let \"w\" be the length of the waltz and \"s\" be that of the sonata, in minutes.\r\n" );
document.write( "Then you have these two equations\r\n" );
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document.write( "4w + 3s = 33,   (1)\r\n" );
document.write( "6w +  s = 25.   (2) \r\n" );
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document.write( "From (2), express s = 25 - 6w and hen substitute it into (1). You will get\r\n" );
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document.write( "4w + 3*(25-6w) = 33,  or\r\n" );
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document.write( "4w + 75 - 18w = 33,  or\r\n" );
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document.write( "-14w = 33-75,\r\n" );
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document.write( "-14w = 42,\r\n" );
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document.write( "w =  = 3.\r\n" );
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document.write( "Answer.  3 minute for the waltz and 25-6w = 25-18 = 7 minutes for the sonatina.\r\n" );
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