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.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.