document.write( "Question 445895: 7 audio cassettes and 3 video cassettes cost rs 1110,while 5 audio cassettes and 4 video cassettes cost rs 1350 find the cost of an audio cassette and a video casette \n" ); document.write( "

Algebra.Com's Answer #853313 by ikleyn(53750) $\"\"$ $\"About$

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\n" ); document.write( "7 audio cassettes and 3 video cassettes cost rs 1110,while 5 audio cassettes and 4 video cassettes cost rs 1350
\n" ); document.write( "find the cost of an audio cassette and a video cassette
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\n" ); document.write( "\n" ); document.write( " In the post by @mananth the solution is incorrect, since equations are written incorrectly.\r
\n" ); document.write( "\n" ); document.write( " I came to do the job accurately.\r
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document.write( "Audio --- x Cost\r\n" );
document.write( "Video --- y Cost\r\n" );
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document.write( "Equations\r\n" );
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document.write( "    7x + 3y = 1110    (1)\r\n" );
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document.write( "    5x + 4y = 1350    (2)\r\n" );
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document.write( "I will solve using the determinant method (= Cramer's method),\r\n" );
document.write( "sinse it is easier to write (no need to write excessive words).\r\n" );
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document.write( "D (the determinant) is         7*4 - 5*3 = 28 - 15 = 13.\r\n" );
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document.write( "Dx (the determinant for x) is  1110*4 - 1350*3 = 390.\r\n" );
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document.write( "Dy (the determinant for y) is  7*1350 - 5*1110 = 3900.\r\n" );
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document.write( "Hence,  x = Dx/D = 390/13 = 30;  y = Dy/D = 3900/13 = 300.\r\n" );
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document.write( "ANSWER.  Audio-cassette costs rs 30;  video-cassette costs rs 300.\r\n" );
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document.write( "CHECK. First  equation, left side is  7*30 + 3*300 = 1110.   ! correct !\r\n" );
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document.write( "       Second equation, left side is  5*30 + 4*300 = 1350.   ! correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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