To find the additional fee per brochure and the printing fee, we can analyze the data provided in the table:
From the table:
- For 40 brochures: Total Cost = $600
- For 43 brochures: Total Cost = $607.50
- For 45 brochures: Total Cost = $612.50
- For 52 brochures: Total Cost = $630
- For 55 brochures: Total Cost = $637.50
Let's first calculate the change in cost when the number of brochures increases:
-
From 40 to 43 brochures:
- Cost change = $607.50 - $600 = $7.50
- Number of brochures change = 43 - 40 = 3
- Additional fee per brochure = Cost change / Number of brochures change = $7.50 / 3 = $2.50
-
From 43 to 45 brochures:
- Cost change = $612.50 - $607.50 = $5.00
- Number of brochures change = 45 - 43 = 2
- Additional fee per brochure = Cost change / Number of brochures change = $5.00 / 2 = $2.50
-
From 45 to 52 brochures:
- Cost change = $630.00 - $612.50 = $17.50
- Number of brochures change = 52 - 45 = 7
- Additional fee per brochure = $17.50 / 7 = $2.50
-
From 52 to 55 brochures:
- Cost change = $637.50 - $630.00 = $7.50
- Number of brochures change = 55 - 52 = 3
- Additional fee per brochure = $7.50 / 3 = $2.50
From the calculations, the additional fee per brochure is consistently determined to be $2.50.
Next, to find the printing fee, we can use the linear cost model: Let \( y = mx + b\), where \( y \) is the total cost, \( m \) is the additional fee per brochure, \( x \) is the number of brochures, and \( b \) is the printing fee.
Using the first point (40, 600): \[ 600 = 2.50(40) + b \] \[ 600 = 100 + b \] \[ b = 600 - 100 = 500 \]
So the printing fee is $500.
Thus, none of the potential answers correctly state the printing fee, but we can conclude from the analysis:
- The correct additional fee per brochure is $2.50.
- The printing fee, derived from the analysis, is $500.
With that, the only true statement from the responses given would be: C The additional fee per brochure is $2.50.
1 answer