Algebra.Com's Answer #827235 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "if x is the set of multiples of 5, and Y is the set of three-digit positive integers
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document.write( "which are  multiples of 7, how many numbers are common to both sets
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document.write( "First such number is 105, and then every 35-th integer number in this sequence of natural numbers\r\n" );
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document.write( " 106, 107, 108, . . . , 998, 999\r\n" );
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document.write( "satisfies the criterion.\r\n" );
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document.write( "So, you calculate this ratio\r\n" );
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document.write( "  = 25.54...\r\n" );
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document.write( "as a decimal, and then you round this decimal to the closest smaller integer, which is 25.\r\n" );
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document.write( " Doing this way, you determine the number of segments of the length of 35 units from 106 to 999.\r\n" );
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document.write( " Each such segment contains one and only one integer number multiple of 5 and 7 simultaneously\r\n" );
document.write( " as the last number of the segment.\r\n" );
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document.write( "Finally add 1 (one), which counts for the number of 105.\r\n" );
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document.write( "So, your answer is 25 + 1 = 26.\r\n" );
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document.write( "Solved and explained.\r
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