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Setting up the right equation is the first and perhaps the most crucial step in solving any math problem. In this particular exercise, we need to find out what percent 20 is of 10. To do this, we first need to establish an unknown variable that will represent the percentage we are looking for. We will denote this unknown percentage as \(x\). Then, the phrase '20 is what percent of 10' can be mathematically written as \[ \frac{x}{100} \times 10 = 20 \]. This equation means that when \(x\) percent of 10 is taken, it equals 20. Therefore, translating a word problem into a math equation involves defining what you're solving for and then expressing conditions in mathematical terms.

Once the equation is set up, the next step is to isolate the variable to find its value. Here, we have the equation \[ \frac{x}{100} \times 10 = 20 \].

To eliminate the fraction, we'll perform algebraic manipulation by multiplying both sides of the equation by 100. This gives us: \[ x \times 10 = 2000 \].

Now, the equation is simplified to a more manageable form. We can then solve for \(x\) by dividing both sides by 10:

\[ x = \frac{2000}{10} = 200 \].

Basic algebraic operations like multiplication and division help us to keep the equation balanced on both sides while making it simpler to find the unknown variable.

Solving mathematical problems can often be simplified by breaking down the process into clear, manageable steps. In our example problem, the following steps were used:

1. **Understand the Problem:** Recognize that we need to find what percentage 20 is of 10.

2. **Set Up the Equation:** Translate the word problem into a mathematical equation using an unknown variable \(x\): \[ \frac{x}{100} \times 10 = 20 \].

3. **Manipulate the Equation:** Perform algebraic operations to isolate the variable. Here, we multiply both sides by 100, then divide by 10 to solve for \(x\).

4. **Verify the Solution:** Ensure the solution makes sense within the context of the problem. In this case, discovering \( x = 200 \) means that 20 is indeed 200% of 10.

By following these organized steps, problem-solving becomes less daunting and more systematic, paving the way for accurate results.