Chapter 8.7, Problem 27PPS

(a)

To determine

To calculate: To write an equation to represent $y$ the total cost of having your photo taken and buying $x$ number of $5\times 7\text{'}$ for each studio

Answer to Problem 27PPS

Equation to represent total cost for Lifetime Photos studio is $y=18+15x$ and for Family Photos studio is $y=12+15x$

Explanation of Solution

Given information: The table showing the prices of sitting fees and each $5\times 7\text{'}$ portrait for two photography studio

Studio	Sitting Fee ($)	$5\times 7\text{'}$ Price ($)
Lifetime Photos	18	15
Family Photos	12	15

Calculation:

Given the table

Studio	Sitting Fee ($)	$5\times 7\text{'}$ Price ($)
Lifetime Photos	18	15
Family Photos	12	15

Let the number of portrait be $x$

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Lifetime Photos studio is

  $y=18+15x$

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Family Photos studio is

  $y=12+15x$

Conclusion:

Hence, the equation to represent total cost for Lifetime Photos studio is $y=18+15x$ and for Family Photos studio is $y=12+15x$

(b)

To determine

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

Answer to Problem 27PPS

Graphs are plotted

Explanation of Solution

Given information: The table showing the prices of sitting fees and each $5\times 7\text{'}$ portrait for two photography studio

Studio	Sitting Fee ($)	$5\times 7\text{'}$ Price ($)
Lifetime Photos	18	15
Family Photos	12	15

Calculation:

Given the table

Studio	Sitting Fee ($)	$5\times 7\text{'}$ Price ($)
Lifetime Photos	18	15
Family Photos	12	15

Let the number of portrait be $x$

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Lifetime Photos studio is

  $y=18+15x$

Solving the above equation:

When $x=0$

  $\begin{array}{l}y=18+15\left(0\right)\\ y=18+0\\ y=18\end{array}$

When $x=1$

  $\begin{array}{l}y=18+15\left(1\right)\\ y=18+15\\ y=33\end{array}$

Points satisfying the equation are $\left(0,18\right)$ and $\left(1,33\right)$

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Family Photos studio is

  $y=12+15x$

Solving the above equation:

When $x=0$

  $\begin{array}{l}y=12+15\left(0\right)\\ y=12+0\\ y=12\end{array}$

When $x=1$

  $\begin{array}{l}y=12+15\left(1\right)\\ y=12+15\\ y=27\end{array}$

Points satisfying the equation are $\left(0,12\right)$ and $\left(1,27\right)$

Plotting both the equation on same coordinate plane,

  

Conclusion:

Hence, the graph of both the equations are plotted.

(c)

To determine

To calculate: To find if the lines will intersect

Answer to Problem 27PPS

The lines of two equations will never intersect

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

Calculation:

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Lifetime Photos studio is

  $y=18+15x$

Slope of line, $m_1=18$

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Family Photos studio is

  $y=12+15x$

Slope of line, $m_2=18$

Since $m_1=m_2$

Thus, line are parallel

Conclusion:

Hence, the lines will never intersect.

(c)

To determine

To calculate: To compare the slope of the lines

Answer to Problem 27PPS

Slopes of both the lines are same.

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

Calculation:

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Lifetime Photos studio is

  $y=18+15x$

Slope of line, $m_1=18$

Equation to represent the total cost $y$ of having your photo taken and buying $x$ number of portrait at Family Photos studio is

  $y=12+15x$

Slope of line, $m_2=18$

Here, $m_1=m_2$

Conclusion:

Hence, the slope of both the lines are same.