## anonymous 4 years ago How many positive integers less than 100 have a remainder of 3 when divided by 7?

1. anonymous

14.

2. anonymous

$3,7+3,2\times 7+3,3\times 7+3,...$

3. anonymous

so abtrehearn is right. since $14\times 7+3=101$ which tells us that there are 13 +1 because of the first one

4. anonymous

Are u counting zero? If so why?

5. anonymous

I'm thinking 13.

6. anonymous

because 7 goes in to 3 zero times with a remainder of 3

7. 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 : ?

8. 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.

9. anonymous

10, 17, 24, ..., 94 That should be 13 terms.

10. 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}.

11. anonymous

I guess I missed the first one, i.e., 3.

12. anonymous

Good job, abtrehearn,

13. anonymous

I'm not sure I understand how 3 works also : /

14. anonymous

Ten-four, IA-MrC :^)