The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 15lb 15⁢lb stretches a certain spring 19in. 19⁢in., how far will the spring stretch if the weight is increased to 30lb 30⁢lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest in.)

Answer: the spring would be stretched by 38 inches.

Step-by-step explanation:

The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. Let L represent the length of the spring and let w represent the weight placed at the end of the spring. Introducing a constant of variation, k, the expression would be

L = kW

If a weight of 15lb stretches a certain spring 19in, the expression would be

19 = 15k

k = 19/15

The equation would be

L = 19w/15

if the weight is increased to 30lb, then the length by which the spring would be stretched is

L = 19 * 30/15

L = 38 inches