To determine how many kilograms of rock samples the astronauts brought back from the moon, we need to convert the weight from pounds (lb) to kilograms (kg). We are provided with the conversion rate that 1 kilogram is equivalent to 2.20 pounds.
Given:
- Weight in pounds (lb) = 500 lb
- Conversion factor = 1 kg = 2.20 lb
Here's the step-by-step solution:
1. Identify the conversion factor: We know that 1 kilogram = 2.20 pounds. To convert pounds to kilograms, we can use the conversion factor [tex]\(\frac{1 \text{ kg}}{2.20 \text{ lb}}\)[/tex].
2. Set up the conversion:
[tex]\[
\text{Weight in kilograms} = \text{Weight in pounds} \times \left( \frac{1 \text{ kg}}{2.20 \text{ lb}} \right)
\][/tex]
3. Substitute the given weight in pounds:
[tex]\[
\text{Weight in kilograms} = 500 \text{ lb} \times \left( \frac{1 \text{ kg}}{2.20 \text{ lb}} \right)
\][/tex]
4. Calculate the weight in kilograms:
[tex]\[
\text{Weight in kilograms} = 500 \text{ lb} \times \frac{1}{2.20}
\][/tex]
5. Simplify the calculation:
[tex]\[
\text{Weight in kilograms} = 500 \text{ lb} \times 0.45454545454545453
\][/tex]
6. Final result:
[tex]\[
\text{Weight in kilograms} \approx 227.27 \text{ kg}
\][/tex]
So, the astronauts brought back approximately 227.27 kilograms of rock samples from the moon.
Therefore, the correct answer among the provided options is:
[tex]\[ 227 \text{ kg} \][/tex]
