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?

6.25

14,400

300

48

Answer 1

To find the constant of variation, we can use the relationship given in the problem. We know that the weight of the object on Earth (W_E) varies directly with its weight on the moon (W_M).

The formula for direct variation can be expressed as:

\[
W_E = k \cdot W_M
\]

where \( k \) is the constant of variation.

Given that:
- \( W_E = 300 \) pounds (weight on Earth)
- \( W_M = 48 \) pounds (weight on the moon)

We can substitute these values into the equation to solve for \( k \):

\[
300 = k \cdot 48
\]

Now, we rearrange the equation to solve for \( k \):

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

Calculating this gives:

\[
k = 6.25
\]

So, the constant of variation is \( \boxed{6.25} \).