**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.**