Chapter 4.2, Problem 33E

a.

To determine

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

Answer to Problem 33E

The equation is $y=80x+145$ .

Explanation of Solution

Given Information: Company charges $\$225$ for first $1000$ stickers and $\$80$ for each additional $1000$ stickers.

Calculation:

Using the given information, a table is made containing data values for printing of $6000$ stickers,

  $\begin{array}{lllllll}x\hfill & 1\hfill & 2\hfill & 3\hfill & 4\hfill & 5\hfill & 6\hfill \\ y\hfill & \$225\hfill & \$305\hfill & \$385\hfill & \$465\hfill & \$545\hfill & \$625\hfill \end{array}$

In the above table, $x$ represents the number of stickers (in thousands) and $y$ represents the total cost incurred,

Point slope formula: $(y-y_1)=m(x-x_1)$

  $m=\frac{y-y_1}{x-x_1}$

Considering two coordinates $(1,225)$ and $(6,625)$ ,

  $\begin{array}{l}m=\frac{625-225}{6-1}\\ m=\frac{400}{5}\\ m=80\end{array}$

Substituting the available values in point slope formula,

  $y-225=80(x-1)$

  $y=80(x-1)+225$ (Arranging)

  $y=80x-80+225$ (Distributive Property)

  $y=80x+145$ (Combining like terms)

Thus, the equation is $y=80x+145$ .

b.

To determine

To find: The total cost of $9000$ stickers.

Answer to Problem 33E

The cost will be $\$865$ .

Explanation of Solution

Given information: $y=80x+145$ (from previous part).

Calculation:

Putting $x=9$ in the equation $y=80x+145$ ,

  $\begin{array}{l}y=80x+145\\ y=80(9)+145\\ y=720+145\\ y=865\end{array}$

Thus, the cost will be $\$865$ .