he weight of an object on the moon varies directly with its weight on the earth. If an object weighs 144 pounds on the earth, it weighs 24 pounds on the moon.
If an object weighs 32 pounds on the moon, how many pounds does it weigh on the earth?
To find the weight of the object on the earth, we can use the equation of variation:
Weight on the moon/Weight on the earth = k
We know that when the weight on the earth is 144 pounds, the weight on the moon is 24 pounds. Therefore, we can write:
24/144 = k
Simplifying this equation gives us:
k = 1/6
Now, let's use this value of k to find the weight on the earth when the weight on the moon is 32 pounds:
32/x = 1/6
Cross multiplying gives us:
6 * 32 = x
Therefore, the weight of the object on the earth is 192 pounds.
To find out how many pounds the object weighs on the earth, we can set up a proportion using the given information.
Let's assume x is the weight of the object on the earth.
We know that the weight on the moon (24 pounds) is directly proportional to the weight on earth (144 pounds). This can be written as:
24/144 = 32/x
To solve for x, we can cross-multiply:
24x = 144 * 32
Divide both sides of the equation by 24:
x = (144 * 32) / 24
x = 192
Therefore, if the object weighs 32 pounds on the moon, it weighs 192 pounds on the earth.
We can solve this problem using direct variation. Direct variation means that two variables are related in such a way that when one variable changes, the other variable changes proportionally.
In this case, the weight of the object on the moon varies directly with its weight on the earth. We can write this relationship as:
Weight on the moon = k * Weight on the earth
where k is the constant of variation.
We are given that when the object weighs 144 pounds on the earth, it weighs 24 pounds on the moon. We can use this information to find the value of k. Plugging the values into the equation, we get:
24 = k * 144
To solve for k, we divide both sides of the equation by 144:
k = 24 / 144
Simplifying this, we get:
k = 1/6
Now we can use this value of k to find the weight of the object on the earth when it weighs 32 pounds on the moon. Plugging the values into the equation, we get:
32 = (1/6) * Weight on the earth
To solve for the weight on the earth, we multiply both sides of the equation by 6:
6 * 32 = Weight on the earth
Simplifying this, we get:
192 = Weight on the earth
Therefore, the object weighs 192 pounds on the earth.