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There are  members in the Trumpington marching band, and when they line up in rows of 26, there are 4 band members left over. If  is an integer and there are fewer than 1000 band members, what is the maximum number of people that could be in the Trumpington marching band?

 Jun 26, 2023
 #1
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Using CRT + MMI

 

26m  +  4, where m=0,1,2,3,.......etc.

[26 * 38] + 4 =988 maximum number of people in the marching band.

 

Check: 988 mod 26 =4 - the remainder.

 Jun 26, 2023
 #2
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What is CRT + MMI?

 Jun 27, 2023
 #3
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And your solution is incorrect, the correct answer is 940. You would have to use multiplicative inverses in your solution.

 Jun 27, 2023
 #4
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0

 

There are  members in the Trumpington marching band, and when they line up in rows of 26, there are 4 band members left over. If  is an integer and there are fewer than 1000 band members, what is the maximum number of people that could be in the Trumpington marching band?       

 

I don't know how to work modulus problems,

I don't think they taught it when I was in school.   

In fact, I never even heard of it until I saw it in this website. 

 

So I'm going to kind of wing it.     

 

There are fewer than 1000 members,  

so start with 999.   

 

Divide 999 by 26 and see what the answer is.   

                                                                                         999 / 26  =  38.423   

 

Take the whole number part of that quotient, 

which is 38, and multiply it by 26. 

                                                                                           38 • 26  =  988   

 

So 988 is the number of band members that will  

fill up 38 rows of 26 members per row with none    

left over.  We need 4 left over, so just add it on.    

                                                                                          988 + 4  =  992   

 

And there you have it.  992 band members is the most,   

short of 1000, that will fit into rows of 26 members per row,     

and have 4 musicians left over.  Probably the piano players;   

those Steinways are hard to trundle around on a football field.

.

 Jun 30, 2023
edited by Bosco  Jun 30, 2023

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