Question

Mario has to take medication for $180days$. The prescription says that he has to take it two days in a row, then skip one day he will repeat this pattern for$180days$. If he begins taking the medicine on a Monday, how many times will he take it on a Monday and then on Tuesday of the same week?​

Answer 1

Compute the required value:

Let's give a number to each day of the week.

Monday$\to 1$

Tuesday$\to 2$

Wednesday $➞3$

Thursday$➞4$

Friday $➞5$

Saturday $➞6$

Sunday $➞7$

Given: He begins taking the medicine on a Monday and he has to take it two days in a row, then skip one day he will repeat this pattern$180days$.

Therefore, the pattern of taking medicine,

$\left(1,2\right)\to \left(4,5\right)\to \left(7,1\right)\to \left(3,4\right)\to \left(6,7\right)\to \left(2,3\right)\to \left(5,6\right)\to \left(1,2\right)......$

We can see that Mario takes medicine again on Monday and Tuesday after two weeks.

There are $25weeks$ and $5days$ in $180days$ if started on Monday.

In $24weeks$, he would take medicine on Monday-Tuesday$12times$ , and he will take one more time in $25week$.

Hence, total $13times$ Mario takes medication on Monday-Tuesday.