Answer:
we have 60 large boxes and 50 small boxes.
Step-by-step explanation:
First, "boxes of two sizes" means we can assign variables:
   Let x = number of large boxes
        y = number of small boxes
Now, "There are 110 boxes in all"    means    x + y = 110
Now, the pounds for each kind of box is:
     (pounds per box)*(number of boxes)
 pounds for large boxes     +    pounds for small boxes      =    4200pounds
                  "the truck is carrying a total of 4200 pounds in boxes"
  
         (45)*(x)                   +              (30)*(y)                  = 4200 
Now, Solve for one of the variables in the first equation then replace (substitute) the expression for that variable in the second.  Let's solve for x:
    x = 110 - y          [from eq1]
  
     45(110-y) + 30y = 4200            [from eq2]
      4950 - 45y  + 30y= 4200         [distribute]
      4950 - 15y = 4200
       -15y = -750
          y = 50           [divide both sides by (-15)]
  
  There are 50 small boxes.
  
Put that value into either equation (now, which is easier?) to solve for x:
   x = 110 - y
   x = 110 - 50
   x = 60
  There are 60 large boxes.
Now, let's verify our solution:
  
Is   60+50= 110 ?       [eq1]
          110 = 110 ? yes!
Is  60(45) + 50(30) = 4125   ?
      2700 + 1500 = 4200 ?
        4200 = 4200 ? yes
So we have 60 large boxes and 50 small boxes.