document.write( "Question 1210396: Hakim spent 3/8 of his money on 3 cupcakes and 8 muffins. Then he spent 4/5 of the remaining money on 15 pieces of waffle. Each cupcake cost 2/3 as much as a muffin. Each piece of waffle cost $0.20 more than a cupcake. What was the cost of a muffin? \n" ); document.write( "
Algebra.Com's Answer #852215 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Most tutors, including me, often ignore where it says this:\r\n" );
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document.write( "\"Also, if possible, provide a 'check' at the end, so check if the values \r\n" );
document.write( "you computed in fact are correct\".\r\n" );
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document.write( "Nearly always, we skip this check.\r\n" );
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document.write( "If we would read and heed that, then perhaps we might use a different \r\n" );
document.write( "method, to make it easier to check.\r\n" );
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document.write( "Hakim spent 3/8 of his money on 3 cupcakes and 8 muffins. Then he spent 4/5\r\n" );
document.write( "of the remaining money on 15 pieces of waffle. Each cupcake cost 2/3 as much as\r\n" );
document.write( "a muffin. Each piece of waffle cost $0.20 more than a cupcake. What was the \r\n" );
document.write( "cost of a muffin?\r\n" );
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document.write( "Let T = total money Hakim had at the beginning.\r\n" );
document.write( "Let C = cost of a cupcake\r\n" );
document.write( "Let M = cost of a muffin\r\n" );
document.write( "Let W = cost of a piece of waffle\r\n" );
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document.write( "Hakim spent 3/8 of his money on 3 cupcakes and 8 muffins. \r\n" );
document.write( "\"expr%283%2F8%29T+=+3C+%2B+8M\"\r\n" );
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document.write( "Then he spent 4/5 of the remaining money\r\n" );
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document.write( "which was \"T+-+%283C+%2B+8M%29\"\r\n" );
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document.write( "on 15 pieces of waffle. \r\n" );
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document.write( "\"expr%284%2F5%29%28T-%283C%2B8M%29%5E%22%22%29=15W\"\r\n" );
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document.write( "Each cupcake cost 2/3 as much as a muffin. \r\n" );
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document.write( "\"C=expr%282%2F3%29M\"\r\n" );
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document.write( "Each piece of waffle cost $0.20 more than a cupcake. \r\n" );
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document.write( "\"W+=+C+%2B+0.20\"\r\n" );
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document.write( "Go to any of the online solvers for systems of equations\r\n" );
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document.write( "https://www.wolframalpha.com/\r\n" );
document.write( "https://www.symbolab.com/solver/system-of-equations-calculator\r\n" );
document.write( "https://cowpi.com/math/systemsolver/4x4.html\r\n" );
document.write( "https://www.wolframalpha.com/calculators/system-equation-calculator\r\n" );
document.write( "There are others also.\r\n" );
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document.write( "Type in \r\n" );
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document.write( "(3/8)T = 3C + 8M,  (4/5)(T-(3C+8M))=15W, C = (2/3)M, W = C+0.20\r\n" );
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document.write( "Press ENTER, get\r\n" );
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document.write( "C = 0.6, M = 0.09, T = 24, W = 0.8 \r\n" );
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document.write( "which we interpret as\r\n" );
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document.write( "C = $0.60, M = $0.90, T = $24.00, W = $0.80.  \r\n" );
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document.write( "What was the cost of a muffin?\r\n" );
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document.write( "$0.90   <--- solved, but not checked.\r\n" );
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document.write( "Now let's check:\r\n" );
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document.write( "Hakim spent 3/8 of his money on 3 cupcakes and 8 muffins.\r\n" );
document.write( "(3/8)x$24.00 = $9.00\r\n" );
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document.write( "3x$0.60 = $1.80, 8x$0.90 = $7.20, $1.80 + $7.20 = $9.00. \r\n" );
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document.write( "That checks.\r\n" );
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document.write( "So his remaining money was $24.00 - $9.00 = $15.00\r\n" );
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document.write( "Then he spent 4/5 of the remaining money \r\n" );
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document.write( "which was (4/5)x$15.00 = $12.00\r\n" );
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document.write( "on 15 pieces of waffle.\r\n" );
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document.write( "15x$0.80 = $12.00 and, indeed, that checks.   \r\n" );
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document.write( "Each cupcake cost 2/3 as much as a muffin. \r\n" );
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document.write( "$0.60 = (2/3)($0.90)\r\n" );
document.write( "$0.60 = $0.60, so that checks.\r\n" );
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document.write( "Each piece of waffle cost $0.20 more than a cupcake.\r\n" );
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document.write( "$0.80 = $0.60 + $0.20\r\n" );
document.write( "$0.80 = $0.80, so that checks. \r\n" );
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document.write( "Now, as you see, everything checks.\r\n" );
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document.write( "Edwin
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