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

1. ## 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.

2. 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.

3. Originally Posted by Prove It
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.