If 12 workers are needed to run 4 machines, how many workers are needed to run 20 machines?

This is a problem involving direct proportionality. The number of workers is directly proportional to the number of machines. If 12 workers are needed to run 4 machines, we can set up a proportion to find how many workers are needed to run 20 machines.

Let \( x \) represent the number of workers needed to run 20 machines.

\[
\frac{12 \, \text{workers}}{4 \, \text{machines}} = \frac{x \, \text{workers}}{20 \, \text{machines}}
\]

Now, solve for \( x \) by cross-multiplying:

\[
12 \times 20 = 4 \times x
\]

\[
240 = 4x
\]

\[
x = \frac{240}{4} = 60
\]

Therefore, 60 workers are needed to run 20 machines.

Would you like more details on proportionality or any other clarifications?

Here are some related questions for further practice:

1. If 15 workers can run 5 machines, how many workers are needed to run 25 machines?
2. If 18 workers run 6 machines, how many workers would run 30 machines?
3. If 8 workers run 2 machines, how many machines can 32 workers run?
4. If 16 workers run 8 machines, how many workers are needed to run 24 machines?
5. If 10 workers are required to run 5 machines, how many workers would be required for 15 machines?

**Tip:** In proportionality problems, remember that when two quantities increase or decrease together, you can use a ratio to find unknown values!

Solve the problem of determining how many workers are needed to run 20 machines when 12 workers are required for 4 machines. This proportionality problem is suitable for Grades 6-8 and demonstrates the use of ratios and cross-multiplication.

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