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