How many natural numbers less than 200 leave a remainder of 3 when divided by 7 and a remainder of 4 when divided by 5?
For the remainder of 3 when divided by 7, look at numbers of the form 7n+3,
the first few are 3,10,17,... get the idea now? You can do the same thing for the ones that leave a remainder of 4 when divided by 5. Then what you can do is compare the two lists and see what numbers are the same.
Thanks, but my teacher doesn't like it when we do trial and error (I mean just comparing two lists) it has to be "clean."
But I like the 7n+3. Would this work?
x=7n+3
x=5n+4
0=2n-1
-2n=-1
2n=1
n=1/2
Well that didn't work is there something kind of like that I could do though?