document.write( "Question 639890: I have five 7 pesos stamps and four 9 pesos stamps. Using one or more of these stamps, find as many different amounts of postage that you can mail with them \n" ); document.write( "
Algebra.Com's Answer #402918 by Edwin McCravy(20060)\"\" \"About 
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document.write( "The problem is more easily read and less confusing if you will use\r\n" );
document.write( "number words for the numerals and numerals for the number word. That is,\r\n" );
document.write( "rewrite the problem with\r\n" );
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document.write( "the numeral \"7\" instead of the word \"seven\", \r\n" );
document.write( "the numeral \"9\" instead of the word \"nine\", \r\n" );
document.write( "the word \"five\" instead of the numeral \"5\",\r\n" );
document.write( "the word \"four\" instead of the numeral \"4\",\r\n" );
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document.write( "like this: \r\n" );
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document.write( "I have 5 seven-peso stamps and 4 nine-peso stamps. Using one or more of these\r\n" );
document.write( "stamps, find as many different amounts of postage that you can mail with them.\r\n" );
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document.write( "There are 5 seven-peso stamps so there are 6 ways to choose the number of \r\n" );
document.write( "seven-peso stamps. The 6 ways are 0, 1, 2, 3, 4, or 5 seven-peso stamps because\r\n" );
document.write( "we must include the use of NONE of them.\r\n" );
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document.write( "There are 4 nine-peso stamps so there are 5 ways to choose the number of\r\n" );
document.write( "nine-peso stamps. The 5 ways are 0, 1, 2, 3, or 4 nine-peso stamps because as\r\n" );
document.write( "above we must include the use of NONE of them.\r\n" );
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document.write( "That would be a total of 6×5 or 30.  And there cannot be two ways to make any\r\n" );
document.write( "sum because seven and nine are relatively prime and there aren't enough of\r\n" );
document.write( "either stamp to make their least common multiple.\r\n" );
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document.write( "However from the 30 we must subtract the case where we use 0 seven-peso stamps\r\n" );
document.write( "and also 0 nine-peso stamps.  0 is not an amount of postage.  \r\n" );
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document.write( "Answer:  29 amounts of postage.  \r\n" );
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document.write( "Edwin
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