Question

The weight of an object on Earth varies directly as the weight of the same object on the moon. A 300 pound object on Earth would weigh 48 pounds on the moon. If an object weighs 75 pounds on the earth, then how much would it weigh on the moon? What is the direct variation equation?

Answer 1

If an object weighs 75 pounds on Earth, it would weigh 12 pounds on the moon. The direct variation equation for the weight relationship between the Earth and the moon is W_moon = (1/6.25) * W_earth.

Step-by-step explanation:

The weight of an object on Earth varies directly as the weight of the same object on the moon. Given that a 300 pound object on Earth would weigh 48 pounds on the moon, we can find the direct variation equation by setting up a proportion: weight on Earth / weight on the moon = constant.

For the given values, we have 300 pounds / 48 pounds = 75 pounds / x pounds. Solving for x gives us x = (48 pounds * 75 pounds) / 300 pounds, which simplifies to x = 12 pounds. Therefore, if an object weighs 75 pounds on Earth, it would weigh 12 pounds on the moon.

The direct variation equation that represents this relationship can be expressed as Wmoon = k * Wearth, where Wmoon is the weight on the moon, Wearth is the weight on Earth, and k is the constant of variation. From the original example, we have k = 48 pounds / 300 pounds, so k = 1/6.25. Thus, the direct variation equation is Wmoon = (1/6.25) * Wearth.