document.write( "Question 1150152: If 6 teddy bears and 5 model planes cost $162 and 5 teddy bears and 6 model planes cost $168, how much will 1 teddy bear and 1 model plane cost? \n" ); document.write( "

Algebra.Com's Answer #771507 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "If 6 teddy bears and 5 model planes cost $162 and 5 teddy bears and 6 model planes cost $168,
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document.write( "    6T + 5M = 162        (1)\r\n" );
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document.write( "    5T + 6M = 168        (2)\r\n" );
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document.write( "Multiply equation (1) by 5 (both sides).\r\n" );
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document.write( "Multiply equation (2) by 6 (both sides).  You will get\r\n" );
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document.write( "    30T + 25M = 5*162    (1')\r\n" );
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document.write( "    30T + 36M = 6*168    (2')\r\n" );
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document.write( "Now subtract equation (1') from equation (2').  The terms \" 30T \" will cancel each other, and you will get\r\n" );
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document.write( "    36M - 25M = 6*168 - 5*162\r\n" );
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document.write( "    11M       = 198\r\n" );
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document.write( "      M       =  = 18.\r\n" );
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document.write( "To find T, substitute M= 18 into equation (1). You will get\r\n" );
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document.write( "    6T + 5*18 = 162\r\n" );
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document.write( "    6T = 162 - 5*18 = 72\r\n" );
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document.write( "     T              =  = 12.\r\n" );
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document.write( "ANSWER.  M = 18;  T = 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On the way, you learned on how the Elimination method works.\r
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\n" ); document.write( "\n" ); document.write( "Below is my notice, written after reading the post by @greenestanps.\r
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\n" ); document.write( "\n" ); document.write( "@greenestamps starts his solution with this sentence\r
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document.write( "    \"Note that the problem does NOT ask you to find the cost of each model plane and each teddy bear. \r\n" );
document.write( "     It only asks you to find the cost of one of each.\"\r\n" );
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\n" ); document.write( "\n" ); document.write( "I do not know how to decipher it \"It only asks you to find the cost of one of each.\"\r
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\n" ); document.write( "\n" ); document.write( "It is exactly what I did: I found the cost of each of the two models.\r
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\n" ); document.write( "\n" ); document.write( "Probably, @greenestamps would like to say \"how much 1 teddy bear and 1 model plane cost TOGETHER ?\"\r
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\n" ); document.write( "\n" ); document.write( "But the problem DOES NOT contain this word \"TOGETHER\".\r
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\n" ); document.write( "\n" ); document.write( "It is his interpretation - one of the two possible interpretations.\r
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\n" ); document.write( "\n" ); document.write( "So, it actually can be treated by any of the two ways.\r
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\n" ); document.write( "\n" ); document.write( "Thus I solved for prices of two models separately;\r
\n" ); document.write( "\n" ); document.write( "@greenestamps solved for the sum of their prices.\r
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\n" ); document.write( "\n" ); document.write( "The question is posed in such uncertain way, that ANY OF THE TWO interpretations works and is admittable.\r
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