Question

The force needed to lift an object varies directly with the weight of the object. To lift an object that weighs 192 pounds, 3 pounds of force is required. At this same rate, how much weight can be lifted with 14 pounds of force?

Answer 1

Using the concept of direct variation, it is determined that 14 pounds of force can lift 896 pounds of weight, given that 3 pounds of force lifts 192 pounds.

Step-by-step explanation:

The student's question pertains to direct variation and involves calculating how much weight can be lifted given a different amount of force based on a rate established by an initial condition. To solve this problem, we use the concept of direct variation, which indicates that as one quantity increases, another quantity increases at a constant rate.

Given the initial condition that 3 pounds of force is needed to lift an object that weighs 192 pounds, we can find the constant of variation, k, by dividing the weight by the force required to lift it:

1. k = weight / force = 192 / 3 = 64 pounds of weight per pound of force.
2. With this constant, we can now find out how much weight can be lifted with 14 pounds of force by multiplying the constant of variation by the new amount of force:
3. Weight = k × force = 64 × 14 = 896 pounds.

Therefore, 14 pounds of force can lift 896 pounds of weight at the same rate.