April 12th, 2014, 12:10 PM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  rest
if we divide n by 7 rest =3 if we divide 5n+4 by 7 what the rest 
April 12th, 2014, 01:28 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,754 Thanks: 695 
5x3 + 4 = 19, mod 7 = 5.

April 12th, 2014, 05:37 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, mared! Quote:
We are told that: $\displaystyle \;n \:=\:7a+3$ for some integer $\displaystyle a.$ Then $\displaystyle \:5n+4 \;=\;5(7a+3)+4 \;=\;35a + 15 + 4 \;=\;35a + 19$ Hence: $\displaystyle \;\frac{5n+4}{7} \;=\; \frac{35a+19}{7} \;=\;5a + 2 + \frac{5}{7}$ Therefore, the remainder is $\displaystyle 5.$  

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