Question

The weight of an object on Earth varies directly with the weight of the same object on the moon. A 300-pound object weighs only 48 pounds on the moon. What is the constant of variation?

Answer 1

To find the constant of variation, we can use the relationship established by the direct variation formula:

\[
W_m = k \cdot W_e
\]

where:
- \( W_m \) is the weight on the moon,
- \( W_e \) is the weight on Earth,
- \( k \) is the constant of variation.

From the problem, we know that:

- \( W_e = 300 \) pounds (weight on Earth),
- \( W_m = 48 \) pounds (weight on moon).

We can rearrange the formula to solve for \( k \):

\[
k = \frac{W_m}{W_e}
\]

Now, substituting the known values:

\[
k = \frac{48}{300}
\]

Calculating this gives:

\[
k = \frac{48 \div 12}{300 \div 12} = \frac{4}{25}
\]

Thus, the constant of variation \( k \) is:

\[
\boxed{\frac{4}{25}}
\]