Description
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50lbs each, and the small boxes weigh 35lbs each. There are 120 boxes in all. If the truck is carrying a total of 5025lbs in boxes, how many of each type of box is it carrying?

Explanation & Answer

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We need to assign variables to what we do not know.
Let x = the number of large boxes weighing 50 lbs.each.
Let y = the number of small boxes weighing 35 lbs each.
If there are 120 boxes in all, that means that x + y = 120, right?
Also notice the relationship: (# of pounds of large boxes) = (50 pounds per box)* x
and (# of pounds of small boxes) = (35 pounds per box)* y
so 50x + 35y = 5025
Our system of equations is
x + y = 120
50x + 35y = 5025
We can solve by substitution.
y = 120 - x
50x + 35*(120 - x) = 5025
50x + 4200 - 35x = 5025
15x + 4200 = 5025
15x = 825
x = 825/15 = 55 large boxes
y = 120 - x = 120 - 55 = 65 small boxes.
Therefore there are 55 large boxes and 65 small boxes.
