Question

Solve the following problems according to the definition of ratio.
If an alloy requires copper, nickel, and zinc in a ratio of 12:5:3, how many kilograms of each metal are needed to make 5 kg of the alloy?

Answer 1

To solve the problem, we will first determine the total parts of the ratio and then use that to find out how much of each metal is needed for 5 kg of the alloy.

The given ratio of copper, nickel, and zinc is 12:5:3.

1. **Calculate the total number of parts in the ratio**:
\[
12 + 5 + 3 = 20 \text{ parts}
\]

2. **Determine the fraction of each metal in the total**:
- Copper: \( \frac{12}{20} \)
- Nickel: \( \frac{5}{20} \)
- Zinc: \( \frac{3}{20} \)

3. **Calculate the amount of each metal needed for 5 kg of the alloy**:
- **Copper**:
\[
\text{Copper} = 5 \, \text{kg} \times \frac{12}{20} = 5 \times 0.6 = 3 \, \text{kg}
\]
- **Nickel**:
\[
\text{Nickel} = 5 \, \text{kg} \times \frac{5}{20} = 5 \times 0.25 = 1.25 \, \text{kg}
\]
- **Zinc**:
\[
\text{Zinc} = 5 \, \text{kg} \times \frac{3}{20} = 5 \times 0.15 = 0.75 \, \text{kg}
\]

4. **Summary of the amounts required**:
- Copper: 3 kg
- Nickel: 1.25 kg
- Zinc: 0.75 kg

Thus, to make 5 kg of the alloy, you will need:
- 3 kg of copper
- 1.25 kg of nickel
- 0.75 kg of zinc