document.write( "Question 1135052: lauren purchased a box of burgers for 35$ at her usual grocery store. When she got back home she saw a flyer for a different store advertising a price that was 50 cents less per burger. if laura has shopped at the second store she could have bought 8 more burgers for the same price\r
\n" ); document.write( "\n" ); document.write( "what was the price of one of the burgers lauren bought? \n" ); document.write( "

Algebra.Com's Answer #752601 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "At the first store the price for one burger was   dollars, where \"n\" was the number of burgers in the box.\r\n" );
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document.write( "At the second store there were (n+8) burgers in their box for the same cost of 35 dollars per box,\r\n" );
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document.write( "so the cost of one single burger was    dollars.   \r\n" );
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document.write( "The difference in price for one single burger is 50 cents = 0.5 dollar, which gives you an equation\r\n" );
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document.write( "     -  = 0.5   dollars.    (1)\r\n" );
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document.write( "To solve this equation, multiply both sides by 2*n*(n+8). You will get\r\n" );
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document.write( "    70(n+8) - 70n = n*(n+8).\r\n" );
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document.write( "Simplify and then solve this quadratic equation\r\n" );
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document.write( "    70n + 70*8 - 70n = n^2 + 8n\r\n" );
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document.write( "    n^2 + 8n - 560 = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (n+28)*(n-20) = 0.\r\n" );
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document.write( "Only positive root  n = 20  is meaningful - so it is the solution.\r\n" );
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document.write( "Answer.  There were 20 burgers in the box at the first store at the price   = $1.75 per one burger.\r\n" );
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document.write( "CHECK.  I will check if the equation (1) is satisfied.\r\n" );
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document.write( "        The price for 1 burger at the first store is   =  cents = 175 cents.\r\n" );
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document.write( "        The price for 1 burger at the second store is   dollars =  = 125 cents, or exactly 0.5 dollars less.\r\n" );
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document.write( "        So the problem is solved correctly (!)\r\n" );
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\n" ); document.write( "\n" ); document.write( "I like this approach: it is short and straightforward, and at every step of building the base equation (1) you follow
\n" ); document.write( "exactly to the problem's description. It prevents you of making errors - as much as possible.\r
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\n" ); document.write( "\n" ); document.write( "In this site, there are several lessons, where you can find similar problems explained ans solved\r
\n" ); document.write( "\n" ); document.write( "    - Challenging word problems solved using quadratic equations \r
\n" ); document.write( "\n" ); document.write( "    - Had they sold . . .\r
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\n" ); document.write( "\n" ); document.write( "Be careful:   The post (the solution) by @swincher4391 has an error !\r
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