Answer:
Step-by-step explanation:
Calculate the slope for both companies (1 and 2) by picking two points from the table for each company and then determine the "Rise/Run."
The costs for both companies:
Cost ($)
Shirts 1 f(x) 2 g(x)
5 117.75 51.75
15 159.25 115.25
Rise 41.5 51.75
Run 10 10
Rise/Run 4.15 6.35
The slopes of these lines are 4.15 and 6.35
Comp. 1: y = 4.15x + b
Comp. 2: y = 6.35x + b
Strangely, both equations have a b that is not zero. This means that, mathematically, there is a cost for doing 0 shirts. Only in America.
One can see this issue by looking at the difference in cost for the first 5 shirts compared to the second set of 5. For Company 1, the first 5 is $117.75, but the second 5 brings us to only a total of $138.50 - a difference of only $20.75. Same with Company 2. The first 5 shirts costs much more than the second five. The third set of 5 shirts (10 - 15) is consistent with the increase with the second set (5-10).
While this doesn't make sense, we must assume there is an initial starting charge, which will be the value of b in the y=mx+b format.
Top calculate b in both equations, enter one of the data points (e.g., (5,117.8) for company 1, and (5,51.75) for company 2 and solve each equation for b.
The results will given these equations:
Company 1: f(x) = 4.15x + 97, and
Company 2: g(x) = 6.35x + 20
Take one shirt into company 1 and you're out $97 before paying for the one laundered shirt. $20 for Company 2.
But each company has a different shirt price:
Company 1: $4.15/shirt
Company 2: $6.35/shirt
We can find the point at which both companies charge the same for x number of shirts by setting the equations equal to each other [i.e., their costs are the same] and solving for x:
4.15x + + 97 = 6.35x + 20
x = 35 shirts
At 35 shirts, both companies will charge $242.30
We can also graph the two equations to find their intersection (both have the same cost). The graph also highlights the absurdity of interpreting anything under 1 shirt. So the range of the functions is x ≥ 1.
See attachment.
