Question

2. Danielle needs 550 copies of her resume printed. Dakota Printing charges $24.50 for the first 250 copies and $12.50 for every 100 additional copies. a. How much will 550 copies cost, including a sales tax of 9 1⁄2 %? Round to the nearest cent. b. If the number of sets of 100 resumes is represented by r, express the cost of the resumes, c(s), algebraically as a piecewise function.

Answer 1

Answer:

$(a)\ Total = \ 67.89$

$(b)$

$c(r) = 24.50(1.095)$ ----- $r \le 2$

$c(r) = [24.50 + (r - 2)*12.50] * [1.095]$ ---- $r > 2$

Explanation:

Given

$Copies = 550$

$First\ 250 = \ 24.50$

$Every\ extra\ 100 = \ 12.50$

Solving (a): Cost of 550 copies

We have:

$First\ 250 = \ 24.50$

This means that, there are 300 copies left (i.e. 550 - 250)

$Every\ extra\ 100 = \ 12.50$

There are 3 hundreds in 300

So, the cost of the 300 copies is:

$300\ copies = 3 * \ 12.50 =\ 37.50$

$Total_{(Before\ Tax)} = First\ 250 + 300\ copies$

$Total_{(Before\ Tax)}= \ 24.50 + \ 37.50$

$Total_{(Before\ Tax)} = \ 62.00$

Apply sales tax of 9.5%

$Total = Total_{(Before\ Tax)} *(1 + Sales\ Tax)$

$Total = \ 62.00 *(1 + 9.5\%)$

Express percentage as decimal

$Total = \ 62.00 *(1 + 0.095)$

$Total = \ 62.00 *(1.095)$

$Total = \ 67.89$

Solving (b): The piece wise function

From the question, we understand that the first 250 cost $24.50

First, we calculate the number of 100s in 250

$r = \frac{250}{100}$

$r =2.5$

r must be an integer; So, we round down

$r =2$

This means that there are 2 whole hundreds in 150.

So, the first function (before tax) is:

$c(r) =24.50$ ---- $r \le 2$

For every other 100 after the first 250

The charge is:

Charge = First 250 + Number of 100s * 12.50

r has a maximum value of 2 for the first 250, this means that the next copies of 100s will have a factor of r - 2

So, the next function (before tax) is:

$c(r) = 24.50 + (r - 2) * 12.50$ ----- $r > 2$

At this point, we have:

$c(r) =24.50$ ---- $r \le 2$

$c(r) = 24.50 + (r - 2) * 12.50$ ----- $r > 2$

Apply sales tax of 9.5%

$c(r) = 24.50(1.095)$ ----- $r \le 2$

$c(r) = [24.50 + (r - 2)*12.50] * [1.095]$ ---- $r > 2$