If John’s elasticity of demand for burgers is constantly 0.9, and he buys 4 burgers when the price is £1.50 per burger, how many will he buy when the price is £1.00 per burger

We are using elasticity to find quantity, instead of the other way around. We will plug in what we know, and solve from there. 

Elasticity = 
And, in the case of John, %Change in Quantity = (X – 4)/4 
Therefore : 
Elasticity = 0.9 = |((X – 4)/4)/(% Change in Price)| 
% Change in Price = (1.00 - 1.50)/(1.50) = -33% 
0.9 = |(X – 4)/4)/(-33%)| 
|((X - 4)/4)| = 0.3 
0.3 = (X - 4)/4 
X = 5.2 

Since John probably can't buy fractions of hot dogs, it looks like he will buy 5 hot dogs when the price drops to £1.00 per hot dog.