the cost of printing 200 business cards is $23.The cost of printing 500 business cards at the same business is $35. Write a linear equation for this information. And to print 700 business cards would cost $

Step-by-step explanation:

The price for printing 700 cards is $15+$700/25 = $43.

Explanation:

We need to MODEL the cost based on the number of cards printed. We will assume that there is a FIXED price

F

for any job (to pay for setup etc.) and a VARIABLE price

V

which is the price to print a single card. The total price

P

will then be

P

=

F

+

n

V

where

n

is the number of cards printed. From the problem statement we have two equations

Equation 1:

23

=

F

+

200

V

and

Equation 2:

35

=

F

+

500

V

Let's solve Equation 1 for

F

F

=

23

−

200

V

and substitute this value for

F

into Equation 2.

35

=

23

−

200

V

+

500

V

Now solve this for

V

.

12

=

300

V

V

=

1

25

We can put this value for

V

into Equation 1 and solve for

F

.

23

=

F

+

200

25

F

=

15

So our model equation is

P

=

15

+

n

25

.

Let's check our answer with the data in the problem.

15

+

200

25

=

23

15

+

500

25

=

35

So we have the correct model equation.

Now use the model to predict the price of printing 700 cards.

15

+

700

25

=

43

.

The price for printing 700 cards is $43.

Note that the price for printing 700 cards is NOT the same as the price for printing 200 cards plus the cost for printing 500 cards! See if you can figure out WHY?

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed

35-60 students are taking math.