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:

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