Payment day problem
My brother Jose gets paid his salary from work every other Friday, but he also receives a bonus of $1000 every time the payment day is one of the first three days of the corresponding month. What is the minimum amount of money due to bonus that he gets in a regular non-leap year? Justify your answer.
The answer is 2000.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Since, he gets paid every other Friday, then he receives at least 26 payments per year ( it can be up to 27 payments if the first payment of the year is on January the 1st). It means that there are at least two months of the year when he gets three payments. On any months when he gets three payments, the first of these payments must be on one of the first three days of the month. That is why the total amount of money due to bonus cannot be less than $2000. He can receive exactly $ 2000 in a year where the first payment is made on January 2nd. It easy to see that in that year the second (and last for the year) payment of a bonus will be July 3rd.