A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 250 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

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.