How do you solve a/an problem like this?

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

1. A.The additional fee per brochure is $7.50.
2. B.The printing fee is $2.50.
3. C.The additional fee per brochure is $2.50.
4. D.The printing fee is $250

Answer 1

Hi!

First you want to set up an equation so you can compare the different rows to solve for the additional fee per brochure or printing fee.

If the total cost (y) is equal to the printing fee (a) plus the additional fee we can use that to set up an equation. First though, to figure out the additional fee, we can make a constant for the additional fee per brochure (b) and we'll multiply it by the number of brochures so you just end up with the total additional fee.

So we have:

y = a + bx

Ok, now you can plug in two different rows of data for x and y so we can solve for a and b.

(600) = a + b(40)

(607.5) = a + b(43)

To solve, you can just subtract the first equation from the second (just subtracting the left side from the left etc) to get:

7.5 = 3b

b = 2.5

Ok, so we know the additional fee per brochure is 2.5.

Luckily we can just stop the problem there because C is one of the options. To continue though you could also solve for a to get a printing fee of $500.

Hope that helps!

Answer 2

Since the only thing that changes in the problem is the cost and number of cards it indicates that the slope and the cost per card is a rate of change. Find the slope and you find the rate of change.

Slope is (Y2 - Y1)/(X2-X1)

(600-607.50)/(40-43) = $2.50

Answer 3

To solve this problem, we need to determine the total cost of printing brochures for Barton Middle School's STEM Night, given the printing fee and the additional fee per brochure printed. Since the relationship between the number of brochures and the total cost is linear, we can represent it using the equation of a line:

\[ \text{Total Cost} = \text{Printing Fee} + (\text{Additional Fee per Brochure}) \times (\text{Number of Brochures}) \]

We are given a table that represents this relationship. Let's say the printing fee is \( p \) (in dollars) and the additional fee per brochure printed is \( b \) (in dollars per brochure).

Since the table shows the linear relationship, we can find the slope (additional fee per brochure) by choosing any two points from the table and calculating the change in total cost divided by the change in the number of brochures.

Once we find the slope, we can plug it into the equation \( y = mx + b \) (where \( y \) is the total cost, \( m \) is the slope, \( x \) is the number of brochures, and \( b \) is the y-intercept representing the printing fee) to find the equation of the line.

Then, we can use this equation to find the total cost for any given number of brochures.

Could you please provide the table with the information about the number of brochures and the total cost?