Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 100 newtons stretches a spring 5cm, how much will a force of 360 newtons stretch the same thing?

We need to write a proportion

1) Force 1 / length 1 = Force 2 / length 2

100 N / 5 cm = 360 N / x cm

x = 5*360/100 = 18 cm

2) Proportion can be written also as

Length 1/Force 1 = Length 2 / Force 2, and it gives the same result

5 cm/100 N=x cm/360 N

x = 5*360/100 = 18 cm