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A rectangular band formation is a formation with m band members in each of r rows, where m and r are integers. A particular band has less than 100 band members. The director arranges them in a rectangular formation and finds that he has two members left over. If he increases the number of members in each row by 1 and reduces the number of rows by 2, there are exactly enough places in the new formation for each band member. What is the largest number of members the band could have?

 

I need this answered quick! thank you!

 Jul 24, 2020
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Let X be total number of membersX = r m (1)X = (m + 1) *(r -2) = r m + r – 2m – (2)(2) – (1): r – 2m – 4 = 0  r = 2m (3)(3) to (2): X = (m+1)(2m+4-2)=2(m+1) (4)Since X < 100, (m+1)2 = X/2 < 50Largest possible integer m is 7. Answer: X = 98
 

 Jul 24, 2020

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