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.
