A factory has three types of machines, each of which works

At first, it might seem as if we don't have enough information to solve. We have 3 unknowns (the rates of Machines A, B, and C), but only 2 equations. Since this is Problem Solving and not Data Sufficiency, though, (and there is no "cannot be determined" answer) there must be some way to solve.

Let's let A = the rate of Machine A, and so on. Construct equations for (number of machines)(hourly rate of machines) = (output per hour per machine)

7 Machine As and 11 Machine Bs can produce 250 widgets per hour --> 7A + 11B = 250
8 Machine As and 22 Machine Cs can produce 600 widgets per hour --> 8A + 22C = 600

As stated before, we have 2 equations for 3 variables, and it looks like we're stuck. But since it's PS, there must be a way to combine them! Simplify the 2nd equation, then combine it with the 1st:

4A + 11C = 300
7A + 11B = 250
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11A + 11B + 11C = 550

--> A + B + C = 50

If we had one of each machine, the 3 together would produce 50 widgets per hour. We don't have to know what each machine does individually.

Since the question asks how many widgets can be produced by these 3 in 8 hrs, (50)(8) = 400.

The answer is A.

Fabio, I definitely agree with your sentiment generally! But Mitch & I have worked side by side for years, with much mutual respect (I'm assuming!). I've never known him to knowingly step on anyone's toes. I'm sure we've all had the experience of someone else posting while we were in the middle of writing, being none the wiser.

AAPL wrote:Veritas Prep

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?

A. 400
B. 475
C. 550
D. 625
E. 700

Letting a, b, and c be the hourly output of Machines a, b, and c, respectively, we can create the equations:

7a + 11b = 250

And

8a + 22c = 600

Multiplying the first equation by 2, we have:

14a + 22b = 500

Adding the two equations together we have:

22a + 22b + 22c = 1100

a + b + c = 50

So in 8 hours the 3 machines can produce 400 widgets.

Answer: A