Answer:
400 widgets.
Step-by-step explanation:
The first thing is to pose the equations that the problem allows us.
Let A, machine As
Let B, machine Bs
Let C, machine Cs
So, we have:
7A + 11B = 250 / hour (1)
8A + 22C = 600 / hour (2)
We have two equations, with 3 unknowns, therefore it cannot be solved by means of a system of equations. But what we can do is make A, B, C have the same quantity.
If we multiply (1) by 2, we are left with:
2 * 7A + 2 * 11B = 2 * 250 / hour
14A + 22B = 500 / hour (3)
We have already achieved that B and C have the same quantity, now for A to be equal, we add (2) and (3). So:
8A + 22C + 14A + 22B = 500 / hour + 600 / hour
22A + 22B + 22C = 1100 / hour
We divide by 22, we have:
A + B + C = 50 / hour
We're asked for (A + B + C) / hour over the course of 8 hours. So multiplying 50 by 8. So
50 / hour * 8 hours = 400
Which means that with As, Bs and Cs machines working at the same time, in 8 hours they make 400 widgets.
