Question 167445
Let the rental charge of single room be 'x' and that of double room be 'y'

    5x + 12 y = 390 ........(i) 

    9x + 10 y = 412 .........(ii)

(i) * 9  & (ii)* 5

       5x *9 + 12y * 9 = 390 * 9 
          45x + 108 y =  3510 ..........(iii)

    9x * 5  + 10y * 5 = 412 *5 
         45 x  + 50 y = 2060  ............(iv)

         (iii) - (iv)

            58y = 1450 

           y  = 1450/ 58 
              = 25 
 substituting y =25 in (i)
        5x + 12 * 25 = 390
                5x = 390-300 = 90
                     x = 90 / 5 = 18 .

Rental charges for single room =$18
rental charges for double room = $ 25