Math_Moron
How many positive integers less than 100 have a remainder of 3 when divided by 7?
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abtrehearn
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14.
anonymous
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\[3,7+3,2\times 7+3,3\times 7+3,...\]
anonymous
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so abtrehearn is right. since
\[14\times 7+3=101\] which tells us that there are 13 +1 because of the first one
Math_Moron
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Are u counting zero? If so why?
LA-MrC
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I'm thinking 13.
anonymous
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because 7 goes in to 3 zero times with a remainder of 3
Math_Moron
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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 : ?
LA-MrC
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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.
LA-MrC
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10, 17, 24, ..., 94
That should be 13 terms.
abtrehearn
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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}.
LA-MrC
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I guess I missed the first one, i.e., 3.
LA-MrC
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Good job, abtrehearn,
Math_Moron
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I'm not sure I understand how 3 works also : /
abtrehearn
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Ten-four, IA-MrC :^)