document.write( "Question 1144398: A band master wished to arrange the band members in pairs for a marching patterns. He found that he was one person short. He tried to arrange by 5s and 7s and he was still one person short. What is the least number of people in the marching band? \n" ); document.write( "

Algebra.Com's Answer #765503 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(corrected response, after reading the problem correctly)

\n" ); document.write( "The number of band members is 1 $\"cross%28more%29\"$ less than a multiple of 5 and 1 $\"cross%28more%29\"$ less than a multiple of 7. Since 5 and 7 are relatively prime (have no common factor), the number of band members is 1 $\"cross%28more%29\"$ less than a multiple of 5*7=35.

\n" ); document.write( "Then, since the number of band members is odd (1 $\"cross%28more%29\"$ less than a multiple of 2), the smallest possible number of band members is the smallest odd number that is 1 $\"cross%28more%29\"$ less than a multiple of 35.

\n" ); document.write( "ANSWER: $\"cross%282%2835%29%2B1%29\"$ 2(35)-1 = 69 \n" ); document.write( "

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