Question

The school art club at a large high school is in charge of designing school T-shirts and getting them printed this year. A local business charges $35 to set up their T-shirt printing machine with the design and $4.25 in materials per T-shirt to print.

1). Create an equation to represent the average cost C(x), in dollars, per T-shirt if x T-shirts are printed by this business.
2). what is the average cost per shirt to print 25 shirts? 100 shirts?
3). what is the cheapest the average cost per T-shirt will get? Explain or show your reasoning.

Answer 1

Total cost includes initial charge for printer set up and material cost.

• C(x) = 4.25x + 35 represents the total cost, where C(x) is the cost of x T- shirts.

Part 1

Average cost per T-shirt is

• C(x)/ x = (4.25x + 35)/x = 4.25 + 35/x

Part 2

Average cost to print 25 T-shirts

• 4.25 + 35/25 = $5.65

Average cost to print 100 T-shirts

• 4.25 + 35/100 = $4.60

Part 3

The average cost 4.25 + 35/x depends on the number of T-shirts printed.

The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.