Allison's middle school team has designed t-shirts containing their team name and color. Allison and her friend Nicole have volunteered to call local stores to get an estimate on the total cost of purchasing t-shirts. Print-o-roma charges a set-up fee, as well as a fixed amount for each shirt ordered. The total cost is shown below for the given number of shirts. Value t's and More charges $8 per shirt. Which company should they use?

Print-o-roma charges a set-up fee plus a fixed price for each shirt. From the table we can see that the cost to order 10 shirts is $95 and for 50 shirts is $ 375. Using these two data points we can calculate the equation which can show the cost of x t-shirts from Print-o-roma. For this first we need to calculate the slope. Slope is defined as:

[tex]Slope=m=\frac{\text{Difference of y-coordinates}}{\text{Difference of x coordinates}}[/tex]

Using the two points: (10, 95) and (50, 375), we get:

[tex]m=\frac{375-95}{50-10}=7[/tex]

This means, slope of the line is 7. Using the point slope form of the equation of a line with m = 7 and point (10, 95), we get:

y - 95 = 7(x - 10)

y = 7x - 70 + 95

y = 7x + 25

Here,

Slope(7) represents the fixed cost of each shirt ordered and y-intercept(25) represents the set-up cost.

Value t's and More Store:

Value t's and More charges $8 per shirt with no set up charges. So for x shirts, this store will charge $ 8x. i.e. total cost y would be:

y = 8x

Comparison:

Since Print-o-roma charges $7 per shirt, in long run and for large orders this company would be a better choice. We can find after how many shirts will Print-o-roma charge overall lesser price than Value t's and More:

Cost of Print-o-roma ≤ Cost of Value t's and More

7x + 25 ≤ 8x

25 ≤ x

This can also be written as:

x ≥ 25

This means, for 25 t-shirts the charges of both stores would be the same. But if the number of t-shirts is more than 25, Print-o-roma will be charging lesser price to print the shirts.