Chapter 9.5, Problem 32IP

a.

To determine

To write an equation representing the total cost $\text{y}$ for $\text{x}$ students at each park.

Answer to Problem 32IP

The cost at Wild Waves is $\text{y}=\text{16}\text{.50x}+\text{200}$ and the cost at Coaster Haven is $\text{y}=\text{14}\text{.50x}+\text{250}$ .

Explanation of Solution

Given information:

The table shows the bus prices to travel to each park and the admission price per student.

  

The equation representing the cost at Wild Waves is:

  $\text{y}=\text{16}\text{.50x}+\text{200}$

The equation representing the cost at Coaster Haven is:

  $\text{y}=\text{14}\text{.50x}+\text{250}$

b.

To determine

To graph the equations.

Explanation of Solution

Given information:

The given equations are:

The equation representing the cost at Wild Waves is $\text{y}=\text{16}\text{.50x}+\text{200}$

The equation representing the cost at Coaster Haven is $\text{y}=\text{14}\text{.50x}+\text{250}$

Graph:

  

Interpretation:

The lines seem to meet at $\text{x}=25$ , so the cost for both the trips would be same for $25$ students.

c.

To determine

To find which trip would cost less if the number of students are given.

Answer to Problem 32IP

The trip at Wild Waves will cost less if $20$ students take the trip.

The trip at Coaster Haven will cost less if $28$ students take the trip.

Explanation of Solution

Given information:

The given statement is:

“If $20$ students decide to take the trip, which trip will cost less? If $28$ students decide to take the trip, which trip will cost less?”

The equations representing the cost for both the trips are:

Wild Waves: $\text{y}=\text{16}\text{.50x}+\text{200}$

Coaster Haven: $\text{y}=\text{14}\text{.50x}+\text{250}$

Calculation:

The cost for both the trips if $20$ students decide to take the trip:

  $\begin{array}{l}\text{Cost at Wild Waves:}\\ \text{y}=\text{16}\text{.50x}+\text{200}\\ \text{y}=\text{16}\text{.50}\left(20\right)+\text{200}\\ \text{y}=530\\ \text{Cost at Coaster Haven:}\\ \text{y}=\text{14}\text{.50x}+\text{250}\\ \text{y}=\text{14}\text{.50}\left(20\right)+\text{250}\\ \text{y}=540\end{array}$

Hence, the trip at Wild Waves will cost less if $20$ students take the trip.

The cost for both the trips if $28$ students decide to take the trip:

  $\begin{array}{l}\text{Cost at Wild Waves:}\\ \text{y}=\text{16}\text{.50x}+\text{200}\\ \text{y}=\text{16}\text{.50}\left(28\right)+\text{200}\\ \text{y}=662\\ \text{Cost at Coaster Haven:}\\ \text{y}=\text{14}\text{.50x}+\text{250}\\ \text{y}=\text{14}\text{.50}\left(28\right)+\text{250}\\ \text{y}=656\end{array}$

Hence, the trip at Coaster Haven will cost less if $28$ students take the trip.

d.

To determine

To state if the results of part c was possible by examining the graph in part b.

Answer to Problem 32IP

The difference in slope of both the equations of the graph is very small, so both the lines appear to be together. But closely looking, it is evident that the cost of Coaster Haven will decrease if the number of students are more than $25$ .

Explanation of Solution

Given information:

The graph obtained in part b is:

  

The trip at Wild Waves will cost less if $20$ students take the trip.

The trip at Coaster Haven will cost less if $28$ students take the trip.

The difference in slope of both the equations of the graph is very small, so both the lines appear to be together. But closely looking, it is evident that the cost of Coaster Haven will decrease if the number of students are more than $25$ .