The cost of printing the school newspaper is $500 for 800 copies and $620 for 1200 copies. If the printing cost is a linear function of the copies printed, how do you find the cost of printing 1500 copies?

Question

Eva Adamson · Accepted Answer

Cost of printing #1500# copies is # $710 #

This is a linear function, i.e obeys straight line equation:

Let y denotes cost in #$# and x denotes number of copies.

Slope #m= (620 -500)/(1200-800)= 120/400=3/10#

Equation of straight line is #y=mx+c or 500 = 3/10*800+c or 500 =240+c or c= 500-240=260# Equation of straight line is # y = 3/10 x+260#

Check: #620 = 3/10*1200 +260 or 620 =360+260 or 620 =620#

Cost of printing #1500# copies is # y =3/10*1500+260 = 450+260 = $710 # graph{3/10 x+260 [-1280, 1280, -640, 640]} [Ans]

Hazel Anglin · Answer

undefined To find the linear function representing the printing cost, we first need to determine the rate of change, or slope, which is the change in cost divided by the change in the number of copies.

First, find the slope:
Slope = (Change in cost) / (Change in number of copies)
Slope = (620 - 500) / (1200 - 800)
Slope = 120 / 400
Slope = 0.3

Now that we have the slope, we can use the point-slope form of a linear equation to find the cost of printing 1500 copies.
Point-slope form: y - y1 = m(x - x1)
Where:
y = printing cost
x = number of copies
m = slope
(x1, y1) is a point on the line.

We can use either of the given points (800, 500) or (1200, 620). Let's use (800, 500).
y - 500 = 0.3(x - 800)

Now, substitute x = 1500 into the equation to find the cost of printing 1500 copies.
y - 500 = 0.3(1500 - 800)
y - 500 = 0.3(700)
y - 500 = 210
y = 210 + 500
y = 710

Therefore, the cost of printing 1500 copies is $710.