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

`(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`

Step-by-step 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 = (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`