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
40
43
45
52
55
Total Cost, y
$600.00
$607.50
$612.50
$630.00
$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.
To determine the printing fee and the additional fee per brochure, we need to find the equation of the linear relationship between the number of brochures and the total cost.
Using the given values, we can calculate the slope of the line:
For (40, $600.00) and (43, $607.50): slope = ($607.50 - $600.00) / (43 - 40) = $7.50 / 3 = $2.50
For (43, $607.50) and (45, $612.50): slope = ($612.50 - $607.50) / (45 - 43) = $5.00 / 2 = $2.50
For (45, $612.50) and (52, $630.00): slope = ($630.00 - $612.50) / (52 - 45) = $17.50 / 7 ≈ $2.50
For (52, $630.00) and (55, $637.50): slope = ($637.50 - $630.00) / (55 - 52) = $7.50 / 3 = $2.50
Since the slope remains constant at $2.50, this represents the additional fee per brochure.
To find the printing fee, we can use any point on the line. Let's use (40, $600.00):
Total cost = Printing fee + (Additional fee per brochure * Number of brochures)
$600.00 = Printing fee + ($2.50 * 40)
$600.00 = Printing fee + $100.00
Printing fee = $600.00 - $100.00 = $500.00
Based on the calculations, the correct statement is:
D. The printing fee is $500.