anonymous
  • anonymous
How many positive integers less than 100 have a remainder of 3 when divided by 7?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
14.
anonymous
  • anonymous
\[3,7+3,2\times 7+3,3\times 7+3,...\]
anonymous
  • anonymous
so abtrehearn is right. since \[14\times 7+3=101\] which tells us that there are 13 +1 because of the first one

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anonymous
  • anonymous
Are u counting zero? If so why?
anonymous
  • anonymous
I'm thinking 13.
anonymous
  • anonymous
because 7 goes in to 3 zero times with a remainder of 3
anonymous
  • anonymous
I was thinking what LA-Mrc said but my book says the answer is 14. If 7 doesn't go into 3 wouldn't the remainder be 7 : ?
anonymous
  • anonymous
Here's how I worked it out: 10 is the first positive integer that can be divide by 7 with a remainder of 3. The next is 17, then 24, ... all the way to 94.
anonymous
  • anonymous
10, 17, 24, ..., 94 That should be 13 terms.
anonymous
  • anonymous
The number 3 is also in the list of positive integers less than 100 whose remainder is 3 upon dividing by 7. The list is {3, 10, 17, ... , 94}.
anonymous
  • anonymous
I guess I missed the first one, i.e., 3.
anonymous
  • anonymous
Good job, abtrehearn,
anonymous
  • anonymous
I'm not sure I understand how 3 works also : /
anonymous
  • anonymous
Ten-four, IA-MrC :^)

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