document.write( "Question 1078289: If a bottle and a glass balance with a pitcher, a bottle balances with a glass and a plate, and two pitchers balance with three plates, can you figure out how many glasses will balance with a bottle? \n" ); document.write( "

Algebra.Com's Answer #692809 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "If a bottle and a glass balance with a pitcher, a bottle balances with a glass and a plate, and two pitchers balance with three plates,
\n" ); document.write( "can you figure out how many glasses will balance with a bottle?
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\n" ); document.write( "\n" ); document.write( "Yes I can.\r
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document.write( "Let b = mass of bottle;\r\n" );
document.write( "    g = mass of glass;\r\n" );
document.write( "    p = mass of pitcher;\r\n" );
document.write( "    L = mass of plate.\r\n" );
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document.write( "Then from the condition, you have these 3 equations for 4 variables:\r\n" );
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document.write( "b + g = p,              (1)\r\n" );
document.write( "b = g + L,              (2)\r\n" );
document.write( "2p = 3L.                (3)\r\n" );
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document.write( "From (1) and (3) you have\r\n" );
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document.write( "b + g = .          (4)\r\n" );
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document.write( "From (2) you have \r\n" );
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document.write( "L = b - g.              (5)\r\n" );
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document.write( "Substitute (5) into (4) replacing and eliminating L. You will get\r\n" );
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document.write( "b + g = .       (6)\r\n" );
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document.write( "Simplify (6):\r\n" );
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document.write( "2b + 2g = 3b - 3g  --->  5g = b.\r\n" );
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document.write( "Answer.  5 glasses balance 1 bottle.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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