document.write( "Question 623154: If 530 pesos can buy 4 kg of fish and 2 kg of pork while 875 pesos can buy 7 kg of fish and 3 kg of pork, how much does a kg of fish cost? \n" ); document.write( "
Algebra.Com's Answer #392025 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "The Problem:\r\n" );
document.write( "If 530 pesos can buy 4 kg of fish and 2 kg of pork while 875 pesos can buy 7 kg of fish and 3 kg of \r\n" );
document.write( "pork, how much does a kg of fish cost?\r\n" );
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document.write( "A Solution:\r\n" );
document.write( "Let f be the cost of a kg of fish (in pesos)\r\n" );
document.write( "Let p be the cost of a kg of pork (in pesos)\r\n" );
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document.write( "We need to write two equations using the information in the problem.\r\n" );
document.write( "530 pesos can buy 4 kg of fish and 2 kg of pork.\r\n" );
document.write( "The cost of 4 kg of fish is 4 times the cost per kg, or 4f.\r\n" );
document.write( "The cost of 2 kg of pork is 2 times the cost per kg, or 2p.\r\n" );
document.write( "[the cost for 4 kg fish] + [cost for 2 kg pork] = [530 pesos]\r\n" );
document.write( "In algebra, we express this relationship as\r\n" );
document.write( "4f + 2p = 530\r\n" );
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document.write( "875 pesos can buy 7 kg of fish and 3 kg of pork.\r\n" );
document.write( "Using similar reasoning, we can write a second equation.\r\n" );
document.write( "7f + 3p = 875.\r\n" );
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document.write( "We now have a system of two equations. We will use the elimination method to solve the system.\r\n" );
document.write( "Multiply every term in the first equation by 3, and every term in the second equation by -2.\r\n" );
document.write( "4f + 2p = 530 -------------->  12f +  6p  =  1590\r\n" );
document.write( "7f + 3p = 875 --------------> -14f + -6p  = -1750\r\n" );
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document.write( "Add the two equations together. Notice that 6p+ -6p is 0, so the p terms are eliminated.\r\n" );
document.write( "-2f = -160\r\n" );
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document.write( "Divide both sides of the equation by -2.\r\n" );
document.write( "f = -160/-2\r\n" );
document.write( "f = 80\r\n" );
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document.write( "A kg of fish costs 80 pesos. We can find the cost of a kg of pork by substituting 80 for f in either \r\n" );
document.write( "equation. I'll use the first one.\r\n" );
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document.write( "4f + 2p = 530\r\n" );
document.write( "4(80) + 2p = 530\r\n" );
document.write( "320 + 2p = 530\r\n" );
document.write( "2p = 530 - 320\r\n" );
document.write( "2p = 210\r\n" );
document.write( "p = 105\r\n" );
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document.write( "A kg of pork costs 105 pesos.\r\n" );
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document.write( "Check your work by substituting 80 for f and 105 for p in the two original equation. \r\n" );
document.write( "(I'll leave that for you to do.)\r\n" );
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document.write( "Feel free to email if you have questions about this solution\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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