Question

The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 3 lb stretches a certain spring 10 in., how far will the spring stretch if the weight is increased to 48 lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest inch.)

A) 160 in.
B) 120 in.
C) 80 in.
D) 40 in.

Answer 1

To determine the new stretch length for a different weight using direct variation, we calculate the new stretch as the product of the variation constant (found from the original weight and stretch) and the new weight. For a 48 lb weight, the spring will stretch 160 inches.

Step-by-step explanation:

The question deals with the concept of direct variation, which is a concept from mathematics. To find how far a spring will stretch when a different weight is applied, you first need to find the variation constant. The variation constant is the ratio of the stretch of the spring to the weight applied. Given that a 3 lb weight stretches the spring 10 inches, the constant can be represented as k = stretch/weight.

In this instance, k = 10 in / 3 lb. Now, to find out how far the spring will stretch for a 48 lb weight, we calculate: stretch = k × weight. Using our variation constant, k = 10/3, we find that the new stretch for a 48 lb weight is stretch = (10/3) × 48 lb.

When simplified, this gives a stretch of 160 inches. As per the choices provided, rounding off to the nearest inch (which is not necessary in this case), the answer is still 160 inches (Option A).