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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.

Sagot :

MrRoyal

Answer:

[tex](a)\ Total = \$67.89[/tex]

[tex](b)[/tex]

[tex]c(r) = 24.50(1.095)[/tex] ----- [tex]r \le 2[/tex]

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

Explanation:

Given

[tex]Copies = 550[/tex]

[tex]First\ 250 = \$24.50[/tex]

[tex]Every\ extra\ 100 = \$12.50[/tex]

Solving (a): Cost of 550 copies

We have:

[tex]First\ 250 = \$24.50[/tex]

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

[tex]Every\ extra\ 100 = \$12.50[/tex]

There are 3 hundreds in 300

So, the cost of the 300 copies is:

[tex]300\ copies = 3 * \$12.50 =\$37.50[/tex]

[tex]Total_{(Before\ Tax)} = First\ 250 + 300\ copies[/tex]

[tex]Total_{(Before\ Tax)}= \$24.50 + \$37.50[/tex]

[tex]Total_{(Before\ Tax)} = \$62.00[/tex]

Apply sales tax of 9.5%

[tex]Total = Total_{(Before\ Tax)} *(1 + Sales\ Tax)[/tex]

[tex]Total = \$62.00 *(1 + 9.5\%)[/tex]

Express percentage as decimal

[tex]Total = \$62.00 *(1 + 0.095)[/tex]

[tex]Total = \$62.00 *(1.095)[/tex]

[tex]Total = \$67.89[/tex]

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

[tex]r = \frac{250}{100}[/tex]

[tex]r =2.5[/tex]

r must be an integer; So, we round down

[tex]r =2[/tex]

This means that there are 2 whole hundreds in 150.

So, the first function (before tax) is:

[tex]c(r) =24.50[/tex] ---- [tex]r \le 2[/tex]

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:

[tex]c(r) = 24.50 + (r - 2) * 12.50[/tex] ----- [tex]r > 2[/tex]

At this point, we have:

[tex]c(r) =24.50[/tex] ---- [tex]r \le 2[/tex]

[tex]c(r) = 24.50 + (r - 2) * 12.50[/tex] ----- [tex]r > 2[/tex]

Apply sales tax of 9.5%

[tex]c(r) = 24.50(1.095)[/tex] ----- [tex]r \le 2[/tex]

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

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