Question

Martha is printing brochures for Barton Middle School’s STEM Night. The printing company charges a printing fee plus an additional fee per brochure printed. The table shows the linear relationship between the number of brochures and the total cost of printing, including the printing fee.



Printing

Number of Brochures, x Total Cost, y
40 $600.00
43 $607.50
45 $612.50
52 $630.00
55 $637.50


Which statement is true?
Responses
A The additional fee per brochure is $7.50.The additional fee per brochure is $7.50.
B The printing fee is $2.50.The printing fee is $2.50.
C The additional fee per brochure is $2.50.The additional fee per brochure is $2.50.
D The printing fee is $250.

Answer 1

To determine the correct statements about the printing fees, we need to analyze the table and use the information given.

We can assume that the total cost \( y \) can be expressed as:
\[
y = mx + b
\]
where:
- \( m \) is the additional fee per brochure,
- \( x \) is the number of brochures,
- \( b \) is the printing fee.

Let's choose two points from the table to find the slope (additional cost per brochure). We'll use the points (40, 600) and (43, 607.50).

1. Find the change in cost:
- From \( y = 600 \) to \( y = 607.50 \), the change in \( y \) is:
\[
607.50 - 600 = 7.50
\]

2. Find the change in the number of brochures:
- From \( x = 40 \) to \( x = 43 \), the change in \( x \) is:
\[
43 - 40 = 3
\]

3. Compute the slope \( m \):
\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{7.50}{3} = 2.50
\]

So, the additional fee per brochure is \( \text{m} = 2.50 \).

Next, we can find the printing fee \( b \) using one of the points, say (40, 600):
\[
600 = 2.50(40) + b
\]
\[
600 = 100 + b
\]
\[
b = 600 - 100 = 500
\]

Now we can summarize our findings:
- The additional fee per brochure is $2.50 (which confirms C).
- The printing fee is $500 (not listed in the options).

Based on the statements provided, only **C** is correct:

C: The additional fee per brochure is $2.50.