A photocopy shop charges [tex]$P 0.60$[/tex] per page for orders of less than 30 pages, [tex]$P 0.50$[/tex] per page for orders of 30 to 60 pages, and [tex]$P 0.40$[/tex] per page for orders of more than 60 pages. Which function best represents the cost [tex]$C(x)$[/tex] for [tex]$x$[/tex] pages of photocopies?

A.
[tex]\[
C(x) = \left\{
\begin{array}{llr}
0.60x & \text{if} & 0 \ \textless \ x \ \textless \ 30 \\
0.50x & \text{if} & 30 \leq x \ \textless \ 60 \\
0.40x & \text{if} & x \geq 60
\end{array}
\right.
\][/tex]

B.
[tex]\[
C(x) = \left\{
\begin{array}{llr}
0.60x & \text{if} & 0 \ \textless \ x \leq 30 \\
0.50x & \text{if} & 31 \ \textless \ x \ \textless \ 60 \\
0.40x & \text{if} & x \geq 61
\end{array}
\right.
\][/tex]

C.
[tex]\[
C(x) = \left\{
\begin{array}{llr}
0.60x & \text{if} & 0 \ \textless \ x \leq 30 \\
0.50x & \text{if} & 31 \ \textless \ x \leq 60 \\
0.40x & \text{if} & x \ \textgreater \ 61
\end{array}
\right.
\][/tex]

Choose an answer.

Question

02-08-2024
Mathematics

Answered

A photocopy shop charges [tex]$P 0.60$[/tex] per page for orders of less than 30 pages, [tex]$P 0.50$[/tex] per page for orders of 30 to 60 pages, and [tex]$P 0.40$[/tex] per page for orders of more than 60 pages. Which function best represents the cost [tex]$C(x)$[/tex] for [tex]$x$[/tex] pages of photocopies?

A.
[tex]\[
C(x) = \left\{
\begin{array}{llr}
0.60x & \text{if} & 0 \ \textless \ x \ \textless \ 30 \\
0.50x & \text{if} & 30 \leq x \ \textless \ 60 \\
0.40x & \text{if} & x \geq 60
\end{array}
\right.
\][/tex]

B.
[tex]\[
C(x) = \left\{
\begin{array}{llr}
0.60x & \text{if} & 0 \ \textless \ x \leq 30 \\
0.50x & \text{if} & 31 \ \textless \ x \ \textless \ 60 \\
0.40x & \text{if} & x \geq 61
\end{array}
\right.
\][/tex]

C.
[tex]\[
C(x) = \left\{
\begin{array}{llr}
0.60x & \text{if} & 0 \ \textless \ x \leq 30 \\
0.50x & \text{if} & 31 \ \textless \ x \leq 60 \\
0.40x & \text{if} & x \ \textgreater \ 61
\end{array}
\right.
\][/tex]

Choose an answer.

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-08-02T02:04:03-04:00

To determine which function best represents the cost [tex]$ C $[/tex] for [tex]$ x $[/tex] pages of photocopies, we need to examine the pricing structure given:

1. The shop charges [tex]$0.60 per page for orders of less than or equal to 30 pages. 2. The shop charges $[/tex]0.50 per page for orders of 31 to 60 pages.
3. The shop charges $0.40 per page for orders of more than 60 pages.

Let's break it down step by step:

1. For orders of [tex]$ 0 < x \leq 30 $[/tex] pages, the cost [tex]$ C $[/tex] is given by:
[tex]\[ C(x) = 0.60x \][/tex]

2. For orders of [tex]$ 31 \leq x \leq 60 $[/tex] pages, the cost [tex]$ C $[/tex] is given by:
[tex]\[ C(x) = 0.50x \][/tex]

3. For orders of [tex]$ x > 61 $[/tex] pages, the cost [tex]$ C $[/tex] is given by:
[tex]\[ C(x) = 0.40x \][/tex]

Considering these points, the correct function to represent the cost [tex]$ C $[/tex] for [tex]$ x $[/tex] pages of photocopies is:
[tex]\[ C(x) = \left\{ \begin{array}{ll} 0.60x & \text{if } 0 < x \leq 30 \\ 0.50x & \text{if } 31 \leq x \leq 60 \\ 0.40x & \text{if } x > 61 \end{array} \right. \][/tex]

Thus, the function that best represents the cost for [tex]$ x $[/tex] pages of photocopies is the third function listed:
[tex]\[ C(x) = \left\{ \begin{array}{ll} 0.60x & \text{if } 0 < x \leq 30 \\ 0.50x & \text{if } 31 < x \leq 60 \\ 0.40x & \text{if } x > 61 \end{array} \right. \][/tex]