document.write( "Question 176305: Chang bought some 25 cent stamps and some 15 cent stamps and paid $5.00. How many 25 cent stamps did he buy? \n" ); document.write( "
Algebra.Com's Answer #131407 by Edwin McCravy(20060)\"\" \"About 
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Chang bought some 25 cent stamps and some 15 cent stamps and paid $5.00. How many 25 cent stamps did he buy?
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document.write( "Let x = the no. of 25 cent stamps and \r\n" );
document.write( "let y = the no. of 15 cent stamps\r\n" );
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document.write( "25x + 15y = 500\r\n" );
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document.write( "5x + 3y = 100\r\n" );
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document.write( "3 is the smallest coefficient in absolute value.\r\n" );
document.write( "So write 5 and 100 in terms of their nearest multiple\r\n" );
document.write( "of 3.  So we write 5 as 6-1 and 100 as 99+1.\r\n" );
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document.write( "\"%286-1%29x+%2B+3y+=+99+%2B+1\"\r\n" );
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document.write( "\"6x+-+x+%2B+3y+=+99+%2B+1\"\r\n" );
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document.write( "Divide every term by 3\r\n" );
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document.write( "\"2x+-+x%2F3+%2B+y+=+33+%2B+1%2F3\"\r\n" );
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document.write( "Isolate all the fractions on the right:\r\n" );
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document.write( "\"2x+%2B+y+-+33+=+x%2F3+%2B+1%2F3\"\r\n" );
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document.write( "The left side must be an integer, say A,\r\n" );
document.write( "so the right side must be equal to \r\n" );
document.write( "integer A also, so\r\n" );
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document.write( "\"2x+%2B+y+-+33+=+A\" and \"x%2F3%2B1%2F3=A\"\r\n" );
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document.write( "Clear the second of fractions by multiplying\r\n" );
document.write( "through by 3:\r\n" );
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document.write( "\"x%2B1=3A\"\r\n" );
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document.write( "Solve for x:\r\n" );
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document.write( "\"x=3A-1\"\r\n" );
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document.write( "Substitute in \"2x+%2B+y+-+33+=+A\"\r\n" );
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document.write( "\"2%283A-1%29%2By-33=A\"\r\n" );
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document.write( "\"6A-2%2By-33=A\"\r\n" );
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document.write( "\"6A%2By-35=A\"\r\n" );
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document.write( "Solve for y\r\n" );
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document.write( "\"y=35-5A\"\r\n" );
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document.write( "So now we have\r\n" );
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document.write( "\"system%28x=3A-1%2Cy=35-5A%29\"\r\n" );
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document.write( "Now since he bought some stamps,\r\n" );
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document.write( "\"x+%3E+0\" and \"y%3E0\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"3A-1%3E0\" and \"35-5A%3E0\"\r\n" );
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document.write( "\"3A%3E1\" and \"-5A%3E-35\"\r\n" );
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document.write( "\"A%3E1%2F3\" and \"A%3C7\"\r\n" );
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document.write( "So since A is an integer \"1%3C=A%3C=6\"\r\n" );
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document.write( "So there are 6 solutions:\r\n" );
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document.write( "A     x=3A-1   y=35-5A\r\n" );
document.write( "1       2         30\r\n" );
document.write( "2       5         25\r\n" );
document.write( "3       8         20 \r\n" );
document.write( "4      11         15 \r\n" );
document.write( "5      14         10\r\n" );
document.write( "6      17          5 \r\n" );
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document.write( "Edwin
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