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?

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- May 6th 2005, 04:34 PMPhilmacAbsolutely no idea how to do this
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?

- May 6th 2005, 05:15 PMbeepnoodle
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. - May 6th 2005, 05:22 PMPhilmac
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?