As the weight held by a spring increases, the length of the spring also increases proportionally. A 2-lb weight stretches a spring to 15 in., and a 12-lb weight stretches the same spring to 20in. What is the length of the spring with no weight attached?

Question

As the weight held by a spring increases, the length of the spring also increases proportionally.  A 2-lb weight stretches a spring to 15 in., and a 12-lb weight stretches the same spring to 20in. What is the length of the spring with no weight attached?

anonymous · Answer

14 inches..
Let initial length be L and elongation per unit of weight be X
Equation 1: L + 2X = 15
Equation 2: L+12X = 20
Thus L = 14