Question

A spring has an original length L inches. When a weight of x pounds is suspended from the spring, its new length y is given by the formula y = L +
x
k
, where k is a constant, measured in pounds per inch.

Solve the formula for x. Show the steps in your work.

The value of k for a certain spring is 2.5. The length of the spring is found to be double its original length when a 10 pound weight is suspended from it. Write the equation for the original length of the spring and solve it. Show the steps in your work.

Answer 1

The way I figured this one out was saying that if it takes 2lbs to stretch it to 12 inches and 5lbs to stretch to 18 inches that means that 3 additional pounds = 6 inches. Therefore, each additional pound is 2 inches. We know already that with 2 lbs it was 12 inches in length and we can also say that 2 lbs = 4 inches. So subtract 4 from 12 and you end up with the answer of 8 inches.