(i) You are the cost Engineer for a construction company in charge of building a new bridge. The construction company will be penalized each day of delay in
construction for bridge. The penalty will be $4500 for the first day and will increase
by $12000 for each following day. Based on its budget, the company can afford to
pay a maximum of $ 155000 toward penalty. By modelling this as an arithmetic
progression, find the maximum number of days by which the completion of work can
be delayed.

The work can only be delayed for 13 days

Step-by-step explanation:

The construction company will be penalized $4500 for delaying the project for the first day after that day the amount will increase by $12000 for each day. The company can only afford to pay $155000 towards the penalty.

Using arithmetic progression,

a = 4500

d = common difference = 12000

nth term = 155000

n = number of days

a + (n - 1)d = 155000

4500 + (n - 1)12000 = 155000

4500 + 12000n - 12000 = 155000

12000n - 7500 = 155000

12000n = 162500

divide both side by 12000

n = 162500/12000

n = 13.5416666667

n = 13.5

The work can only be delayed for 13 days

i assume that by 5 you mean 5 gallons.

(20)(0.25) = 15

removing 15 gallons reduces the tank from 20 to 5.