Chapter 4.2, Problem 33E

(a)

To determine

To write: an equation that represents the total cost of the stickers as a function of the number of stickers ordered.

Answer to Problem 33E

The line equation is C = 80n +145.

Explanation of Solution

Given:

Consider an initial payment of $225 for printing 1000 stickers and $80 for each additional 1000 stickers.

Calculation:

The objective is to write an equation that represents the total cost of stickers as a function of the number of stickers ordered.

For first 1000 stickers, payment is $225

For 2000 stickers, payment is $\$\left(225+80\right)=\$305$ .

For 3000 stickers, payment is $\$\left(305+80\right)=\$385$ .

Let n be number of the stickers and C be the total payment.

Here $n=1$ represents 1000 stickers and $n=1$ represents 2000 stickers.

The common difference between the of stickers $\left(\Delta n\right)$ is,

  $\begin{array}{l}\Delta n=2-1\hfill \\ =1\hfill \end{array}$

The common difference between the total payments $\left(\Delta C\right)$ is,

  $\begin{array}{l}\Delta C=305-225or\Delta C=385-305\\ =80=80\end{array}$

Use the linear equation $C=mn+b$ to find the relation between number of stickers and the total payment.

  $C=mn+b$

Find the value of m

  $\begin{array}{l}m=\frac{\Delta C}{\Delta n}\\ =\frac{80}{1}\\ =80\end{array}$

The line equation is $C=80n+b$

Now find the value of b.

For $n=1$ the value of C is 225, substitute these values in $C=80n+b$ , then

  $\begin{array}{l}225=80\left(1\right)+b\hfill \\ b=225-80\hfill \\ C=145\hfill \end{array}$

Conclusion:

Therefore, the line equation is C = 80n +145.

(b)

To determine

To find: the total cost of 9000 stickers.

Answer to Problem 33E

The costs of the 9000 stickers are $865.

Explanation of Solution

Calculation:

Find the total cost of 9000 stickers.

Since n is given in thousands, Substitute $n=9C=80n+145$

  $\begin{array}{l}C=80n+145\hfill \\ C=80\left(9\right)+145\hfill \\ C=720+145\hfill \\ C=865\hfill \end{array}$

Conclusion:

Therefore, the costs of the 9000 stickers are $865.