Question

An advertiser goes to a printer and is charged $37 for 80 copies of one flyer and $54 for 209 copies of another flyer. The printer

charges a foced setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if 2 is the
number of copies made. C(x)

Answer 1

Answer: c(x) = y = $0.132*x + $27.16

Explanation:

The chargers are a fixed price plus a charge for every copy, then we have a linear relationship.

A linear relationship can be written as:

c(x) = y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, c(x) = y represents the cost in dollars, x is the number of copies bought, and b is the fixed cost.

We know two points in this line:

(80, $37) and (209, $54)

Whit those two points we can find the slope:

a = ($54 - $37)/(209 - 80) = $17/129 = $0.132 per copy.

Then our equation is:

c(x) = y = $0.132*x + b

To find the value of b, we know that 80 copies cost $37, we can replace those values in the equation:

$37 = $0.132*80 + b

$37 = $9.84 + b

($37 - $9.84) = $27.16 = b.

Then the equation is:

c(x) = y = $0.132*x + $27.16