Chapter 4.4, Problem 75AYU

To determine

To calculate:

The number of students to keep the cost per student below or at $\$40$

Answer to Problem 75AYU

Number of students to keep the cost per student below $\$40$ is $50$ .

Explanation of Solution

Given information:

Discount: $\$0.20$

Regular price of ticket: $\$40$

Cost of the bus: $\$500$

Calculation:

Consider,

The number of students to keep the cost per student below or at $\$40$ : $x$

The cost per student is $40-0.2x+\frac{500}{x}$ .

Now, number of students to keep the cost per student below $\$40$ is calculated as:

  $\begin{array}{l}40-0.2x+\frac{500}{x}<40\\ -0.2x+\frac{500}{x}<0\\ \frac{-0.2x^2+500}{x}<0\\ -0.2x^2+500=0\\ -0.2x^2=-500\\ x^2=2500\\ x=50\end{array}$

Thus, at least $50$ students must attend in order to keep the cost per student below $\$40$