55 large boxes
50 small boxes
First, "boxes of two sizes" means we can assign variables:
Let x = number of large boxes
y = number of small boxes
"There are 105 boxes in all" means x + y = 115 [eq1]
Now, the pounds for each kind of box is:
(pounds per box)*(number of boxes)
So,
pounds for large boxes + pounds for small boxes = 7,875 pounds
"the truck is carrying a total of 7,875 pounds in boxes"
(50)*(x) + (25)*(y) = 7,875) eq2]
It is important to find two equations so we can solve for two variables.
Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2. Let's solve for x:
x = 105 - y [from eq1]
50(105-y) + 25y = 4125 [from eq2]
5750 - 50y + 25y = 4125 [distribute]
5750 - 25y = 4125
-25y = -1625
y = 65 [divide both sides by (-25)]
There are 50 small boxes.
Put that value into either equation (now, which is easier?) to solve for x:
x = 115 - y
x = 115 - 65
x = 50
There are 55 large boxes.
Check (very important):
Is 50+65 = 115 ? [eq1]
115 = 115 ?yes
Is 50(50) + 25(65) = 4125 ?
2500 + 1625 = 4125 ?
4125 = 4125 ? yes