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Math Help - if today is Tuesday, what day will it be in 129 days?

  1. #1
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    if today is Tuesday, what day will it be in 129 days?

    Sun=0, Mon=1,....

    2+129\equiv x \ \mbox{(mod 7)}\rightarrow 131\equiv x \ \mbox{(mod 7)}

    Here is what I did, and I obtained the correct answer; however, I think this should have been done another way.

    131-\left \lfloor \frac{131}{7} \right \rfloor*7=5

    131\equiv 5 \ \mbox{(mod 7)}

    In 129 days, it will be Friday.
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  2. #2
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    Every 7 days, you get back to Tuesday.

    Since 129 = 18\cdot 7 + 3 that means that it will be 3 days after Tuesday.

    So the day you'll be on is Friday.
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by Prove It View Post
    Every 7 days, you get back to Tuesday.

    Since 129 = 18\cdot 7 + 3 that means that it will be 3 days after Tuesday.

    So the day you'll be on is Friday.
    To explain Prove It's method a bit further, you're seeking  r such that  0\leq r <7 and  129=7q+r .

     q,r can be found through the division algorithm.
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