#### Answer

40 double rooms and 15 single rooms were rented

#### Work Step by Step

We call x the number of single rooms and y the number of double rooms. Thus, we obtain:
$ x + y = 55 $
And
$ 62x +82y = 4210$
In order to solve this problem, we multiply one or both of the equations by a value that will make one of the variables cancel. We multiply the top equation by -62, and we multiply the bottom equation by 1. Then, we add the two equations to obtain:
$20y = 800 \\ y = 40 $
We plug in the given value into the top equation and solve for the other variable:
$ x + 40 = 55 \\ x =15$