Chapter 13.8, Problem 79STP

To determine

Find the maximum number of days it can be late.

Answer to Problem 79STP

The total number of days it can be late are $57$ .

Explanation of Solution

Given: It is given in the question that a construction company will be fined for each day it is late completing a bridge. The daily fine will be $\$4000$ for the first day and will increase by $\$1000$ each day. Based on its budget, the company can only afford $\$60,000$ in total fines.

Concept Used:

In this, use the concept of using the linear equation and solving the question.

Calculation:

Let the number of day late be x.

The fixed amount that have to fine = $\$4000$ .

The amount that have to pay per day will be $1000x$

Now, according to question,

  $\begin{array}{l}4000+1000x=60000\\ 1000x=60000-4000\\ 1000x=56000\\ x=\frac{56000}{1000}\\ x=56\end{array}$

Since there is also a one day in hand so total days are $56+1=57$ .

Conclusion:

The total number of days are $57$ .