Chapter 8.7, Problem 32PPS

(a)

To determine

To calculate: To write an equation that represent the total cost $y$ for $x$ students at each park.

Answer to Problem 32PPS

Equation to represent total cost for Wild waves park is $y=200+16.50x$ and for Coaster Heaven park is $y=250+14.50x$

Explanation of Solution

Given information: The table showing the bus prices to travel to each park and the admission price per student

Park	Bus Fee($)	Admission Price per student ($)
Wild Waves	200	16.50
Coaster Heaven	250	14.50

Formula Used:

Equation of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given the table

Park	Bus Fee($)	Admission Price per student ($)
Wild Waves	200	16.50
Coaster Heaven	250	14.50

Let the number of students be $x$

Equation to represent the total cost $y$ for $x$ students at Wild Waves park is

  $y=200+16.50x$

Equation to represent the total cost $y$ for $x$ students at Coaster Heavenpark is

  $y=250+14.50x$

Conclusion:

Hence, the equation to represent total cost for Wild waves park is $y=200+16.50x$ and for Coaster Heaven park is $y=250+14.50x$

(b)

To determine

To calculate: To graph the two equations on the same coordinate plane

Answer to Problem 32PPS

Graph is plotted

Explanation of Solution

Given information: The table showing the bus prices to travel to each park and the admission price per student

Park	Bus Fee($)	Admission Price per student ($)
Wild Waves	200	16.50
Coaster Heaven	250	14.50

Formula Used:

Equation of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given the table

Park	Bus Fee($)	Admission Price per student ($)
Wild Waves	200	16.50
Coaster Heaven	250	14.50

Let the number of students be $x$

Equation to represent the total cost $y$ for $x$ students at Wild Waves park is

  $y=200+16.50x$

Solving the above equation:

When $x=0$

  $\begin{array}{l}y=200+16.50\left(0\right)\\ y=200+0\\ y=200\end{array}$

When $x=1$

  $\begin{array}{l}y=200+16.50\left(1\right)\\ y=200+16.50\\ y=216.50\end{array}$

Points satisfying the equation are $\left(0,200\right)$ and $\left(1,216.50\right)$

Equation to represent the total cost $y$ for $x$ students at Coaster Heaven park is

  $y=250+14.50x$

Solving the above equation:

When $x=0$

  $\begin{array}{l}y=250+14.50\left(0\right)\\ y=250+0\\ y=250\end{array}$

When $x=1$

  $\begin{array}{l}y=250+14.50\left(1\right)\\ y=250+14.50\\ y=264.50\end{array}$

Points satisfying the equation are $\left(0,250\right)$ and $\left(1,264.50\right)$

Plotting both the equation on same coordinate plane,

  

Conclusion:

Hence, the graph is plotted.

(c)

To determine

To calculate: To find which trip will cost less if $20$ students decide to take the trip and when $28$ students decide to take the trip.

Answer to Problem 32PPS

When $20$ students decide to take the trip, then trip to Wild Waves Park will cost less and when $28$ students decide to take the trip, then trip to Coaster Heaven Park will cost less.

Explanation of Solution

Given information: The table showing the bus prices to travel to each park and the admission price per student

Park	Bus Fee($)	Admission Price per student ($)
Wild Waves	200	16.50
Coaster Heaven	250	14.50

Formula Used:

Equation of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given the table

Park	Bus Fee($)	Admission Price per student ($)
Wild Waves	200	16.50
Coaster Heaven	250	14.50

Let the number of students be $x$

Equation to represent the total cost $y$ for $x$ students at Wild Waves park is

  $y=200+16.50x$

Equation to represent the total cost $y$ for $x$ students at Coaster Heaven park is

  $y=250+14.50x$

When$20$students decide to take the trip:

Case1: Trip to Wild Waves

Cost is calculated as

  $\begin{array}{l}y=200+16.50\left(20\right)\\ y=200+330\\ y=530\end{array}$

Case1: Trip to Coaster Heaven

Cost is calculated as

  $\begin{array}{l}y=250+14.50\left(20\right)\\ y=250+290\\ y=540\end{array}$

Thus, when $20$ students decide to take the trip, then trip to Wild Waves Park will cost less.

When$28$students decide to take the trip:

Case1: Trip to Wild Waves

Cost is calculated as

  $\begin{array}{l}y=200+16.50\left(28\right)\\ y=200+462\\ y=662\end{array}$

Case1: Trip to Coaster Heaven

Cost is calculated as

  $\begin{array}{l}y=250+14.50\left(28\right)\\ y=250+406\\ y=656\end{array}$

Thus, when $28$ students decide to take the trip, then trip to Coaster Heaven Park will cost less.

Conclusion:

Hence, when $20$ students decide to take the trip, then trip to Wild Waves Park will cost less and when $28$ students decide to take the trip, then trip to Coaster Heaven Park will cost less.