To find out how much the astronaut weighs on the Moon, we can use the ratio of weights on the Moon to Earth.
On Earth, the astronaut weighs 500 pounds, and on the Moon, the ratio of weight is approximately \( \frac{4}{25} \) (since an object weighing 25 pounds on Earth weighs 4 pounds on the Moon).
To calculate the astronaut's weight on the Moon, we can multiply the Earth weight by this ratio:
\[ \text{Weight on Moon} = \text{Weight on Earth} \times \left(\frac{4}{25}\right) \]
Substituting the weight of the astronaut:
\[ \text{Weight on Moon} = 500 \times \left(\frac{4}{25}\right) \]
Calculating:
\[ \text{Weight on Moon} = 500 \times 0.16 = 80 \text{ pounds} \]
Therefore, the astronaut with gear would weigh 80 pounds on the Moon.