Norachai created a mental counting 23% silver by combining two other metals One of these other metals weighed 1mg and contained 34% silver If the other weighed 11mg then what percent of it was silver

Let's solve this problem step by step.

### Step 1: Define the variables.
- Let \( x \) be the percentage of silver in the second metal (the one weighing 11 mg). This is what we're trying to find.
- The first metal weighs 1 mg and contains 34% silver, so the amount of silver in the first metal is:
  \[
  0.34 \, \text{mg}
  \]
- The second metal weighs 11 mg, and since we don't know the percentage of silver in it yet, the amount of silver in the second metal is:
  \[
  0.11x \, \text{mg}
  \]
- The total weight of the combined metals is:
  \[
  1 \, \text{mg} + 11 \, \text{mg} = 12 \, \text{mg}
  \]
- The combined metals contain 23% silver, so the total amount of silver in the mixture is:
  \[
  0.23 \times 12 = 2.76 \, \text{mg}
  \]

### Step 2: Set up the equation.
The total amount of silver in both metals must equal 2.76 mg. Thus, the equation is:
\[
0.34 + 0.11x = 2.76
\]

### Step 3: Solve for \( x \).
Subtract 0.34 from both sides:
\[
0.11x = 2.76 - 0.34
\]
\[
0.11x = 2.42
\]

Now, divide both sides by 0.11:
\[
x = \frac{2.42}{0.11} = 22
\]

### Final Answer:
The percentage of silver in the second metal is **22%**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What happens if the percentage of silver in the first metal is changed?
2. How would the calculation change if the total combined mass were different?
3. What if the second metal had a variable weight? How would that affect the problem?
4. How can you calculate the percentage of a different alloy mixture?
5. Can you determine the overall percentage if the first metal had no silver?

**Tip:** In mixture problems, always ensure the total amount of the desired component (e.g., silver) in the mixture equals the sum of its parts from each individual substance.

Norachai created a mental counting 23% silver by combining two other metals. One of these other metals weighed 1mg and contained 34% silver. If the other weighed 11mg, then what percent of it was silver?

Learn how to calculate the percentage of silver in a metal mixture when combining two different metals. This problem involves algebraic concepts, mixture problems, and percentages, and is suitable for students in Grades 8-10.

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