Question

A construction company will be fined each day of delay in construction for a commercial building. The penalty will be Php5,000 for the first day and will increase by Php1000 for each following day. Based on its budget, the company can afford to pay a maximum of Php50,000 for the fines. Find the maximum number of days by which the completion of work can be delayed.

Answer 1

since this is just an AP with
a = 5000
d = 1000
you want to find n such that
n/2 (2*5000 + 1000(n-1)) <= 50000
or, getting rid of all those zeroes,
n/2 (10+n-1) <= 50
n <= 6

check:
6 days of fines: 5 + 6+7+8+9+10 = 45
7 days = 45 + 11 = 56

Answer 2

I need the answer