Chapter 4.3, Problem 15Q

(a)

To determine

To find: the total costof website.

Answer to Problem 15Q

The total costof websiteis $y=44x+48$

Explanation of Solution

Given:

Charges fee: $48

Company charges $44

Formula Used:

  $y=mx+c$

Calculation:

Consider an initial fee of $48 to set up a website and $44 for monthly maintenance.

For initial (0 month), fee is $48

For first month, fee is $\$\left(48+44\right)=\$92$ .

For second month, fee is $\$\left(92+44\right)=\$136$

Let $x$ be number of month and $y$ be the total cost.

The common difference between the numbers of month $\left(\Delta x\right)$ is 1 and the common difference between the total costs $\left(\Delta y\right)$ is 44.

Use the linear equation $y=mx+c$ to find the relation between number of months and the total costs.

Find the value of $m$

Implies that,

  $\begin{array}{l}m=\frac{\Delta y}{\Delta x}\\ =\frac{44}{1}\\ =44\end{array}$

Hence,

  $y=44x+c$

To find the value of $c$ , pick any paired elements $\left(x,y\right)$ from the break down cost and substitute into $y=44x+c$

Put $x=1$ then $y=92$ into $y=44x+c$

Hence,

  $\begin{array}{l}92=44\left(1\right)+c\hfill \\ c=48\hfill \end{array}$

Therefore, the equation is $\boxed{y=44x+48}$

Conclusion:

Therefore, the total costof websiteis $y=44x+48$

(b)

To determine

To find: the total cost of website for 6 months of maintenance.

Answer to Problem 15Q

Therefore, the total costs for 6 months of maintenance is $\$312$

Explanation of Solution

Calculation:

The total costs for 6 months implies that $x=6$

Then the total cost is,

  $\begin{array}{l}y=44\left(6\right)+48\hfill \\ =312\hfill \end{array}$

Therefore, the total costs for 6 months of maintenance is $\boxed{\$312}$

Conclusion:

Therefore, the total costs for 6 months of maintenance is $\$312$

(c)

To determine

To find: the company to set up and maintain a website

Answer to Problem 15Q

Therefore, to set up and maintain a website with $620 for the greatest amount of time will be with the first company for 13 months

Explanation of Solution

Given:

Company charges: $62

Total amount: $620

Calculation:

Consider another offer with monthly fee for $62 for maintenance without an initial fee.

Let $x$ be number of month and $y$ be the total cost

Implies that,

  $y=62x$

With an amount of $620

For the first company, use $y=44x+48$ to find the number of months $620 can purchase, when $y=620$

  $\begin{array}{l}y=44x+48\hfill \\ 620=44x+48\hfill \\ 44x=572\hfill \\ x=13\hfill \end{array}$

For the second company, use $y=62x$ to find the number of months $620 can purchase, when

  $\begin{array}{l}y=62x\hfill \\ 620=62x\hfill \\ x=10\hfill \end{array}$

Therefore, to set up and maintain a website with $620 for the greatest amount of time will be with the first company for 13 months

Conclusion:

Therefore, to set up and maintain a website with $620 for the greatest amount of time will be with the first company for 13 months