Screen-printing a batch of shirts requires 3 minutes per shirt in addition to 12 minutes of initial set-up time. if it takes 45 minutes to screen-print a batch of shirts,how many shirts are in the batch?

  11 shirts

Step-by-step explanation:

Since 12 of the 45 minute are devoted to setup, the actual printing time is 33 minutes. At 3 minutes per shirt, that's enough time for ...

  (33 min)/(3 min/shirt) = 11 shirts

A batch consists of 11 shirts.

Alternate solution

Another way to consider this is to realize that the setup time is the time required to print 4 shirts. 45 minutes would be enough time to print 45/3 = 15 shirts, but the time for 4 shirts is spent setting up. That leaves the batch size at 15 -4 = 11 shirts.

Let x ft be the dimension of one leg. Then, the other leg will be (x+28) ft.
Applying Pythagoras theory;
Hypotenuse = Sqrt [x^2 +(x+28)^2]

68 = Sqrt [x^2 + x^2+28x+28x+784]
68^2 = 2x^2+56x+784
2x^2 + 56x +784 - 4624 = 0
2x^2 + 56x - 3840 = 0

Solving for x;
x = [-b +/- Sqrt (b^2 -4ac)]/2a where a = 2, b = 56, c = -3840
Then,
x = [-56+/- Sqrt (56^2-4*2*(-3840)]/2*2 = -14+/-46
x = 32 or - 60
Ignoring the negative value, x = 32 ft
Therefore,
One leg dimension = 32 ft
Second leg dimension = 32+28 = 60 ft