Chapter 4.1, Problem 45PPS

(a)

To determine

To Calculate:

The processing fee and write a linear equation to represent the total cost C for t tickets.

Answer to Problem 45PPS

Processing fee = $15

Linear equation of total cost C for t tickets :

  $C=52t+15$

Explanation of Solution

Given Information:

There is a processing fee for each order, and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.

Let

C = Total cost per order = $275

t = Number of tickets ordered = 5

b = The processing fee for each order

m = Cost of each ticket = $52

Formula Used:

Equation of slope-intercept form of a line is given by:

  $y=mx+b\mathrm{............................}(1)$

Where

  $\begin{array}{l}b=y-\mathrm{int}ercept\\ m=\frac{rise}{run}=slope\end{array}$

Calculation:

First , we form the equation :

Let

C = Total cost per order = $275

t = Number of tickets ordered = 5

b = The processing fee for each order

m = Cost of each ticket = $52

Now, we form the equation :

Cost of 1 ticket = $52

So, cost of t tickets = 52t

The processing fee for each order = b

So, the linear equation ( slope-intercept form) of the total cost C , when t tickets purchased per order:

  $C=52t+b\mathrm{..............................}(1)$

Now , we find t by substituting the values in (1)

  $\begin{array}{l}C=275\\ t=5\\ C=52t+b\mathrm{..........................................}[C=275,b=5]\\ \Rightarrow 275=52\cdot 5+b\mathrm{................................}[substituting]\\ \Rightarrow 275=260+b\mathrm{..................................}[simplify]\\ \Rightarrow 275-260=260+b-\mathrm{260...............}[subtract"260"each\_side]\\ \Rightarrow 15=b\mathrm{..............................................}[simplify]\\ or\\ b=15\end{array}$

Hence, the processing fee per order = $15.

Substituting the value in equation (1)

  $\begin{array}{l}b=15\\ C=52t+b\mathrm{...........................}(1)\\ \Rightarrow C=52t+\mathrm{15.....................}[b=15]\end{array}$

The required equation of the total cost C , when t tickets purchased per order:

  $C=52t+\mathrm{15...............................}(2)$

(b)

To determine

To Make :

A table of values for at least three other numbers of tickets.

Explanation of Solution

Given Information:

From part (a)

Equation of the total cost C , when t tickets purchased per order:

  $C=52t+\mathrm{15...............................}(2)$

Calculation:

t	$C(t)=52t+15$	C	(t,C)
1	$C(1)=52(1)+15$	67	(1,67)
2	$C(2)=52(2)+15$	119	(2,119)
3	$C(3)=52(3)+15$	174	(3,174)
4	$C(4)=52(4)+15$	223	(4,223)

(c)

To determine

To Graph and Find : The equation $C=52t+15$ .

Find cost of 8 tickets.

Answer to Problem 45PPS

Cost of 8 tickets = $431

Explanation of Solution

Given Information:

From part (a) and (b)

Equation of the total cost C , when t tickets purchased per order:

  $C=52t+15$

And points on the line are (1,67) , (2,119)

Graph:

To graph the equation, plot the points (1,67) , (2,119) .

  

Now , draw a line to connect the points .

  

Calculate:

To find cost for 8 tickets:

  $\begin{array}{l}C=52t+\mathrm{15...............................}(2)\\ \Rightarrow C=52(8)+\mathrm{15.......................}[t=8]\\ \Rightarrow C=416+\mathrm{15..........................}[simplify]\\ \Rightarrow C=\mathrm{431.................................}[simplify]\end{array}$

Hence, cost of 8 tickets is $431