Question

A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 60 pounds. The truck is transporting 70 large boxes and 60 small boxes. If the truck is carrying a total of 4000 pounds in boxes, how much does each type of box weigh?

Answer 1

• large: 40 lbs
• small: 20 lbs

Explanation:

A system of equations can be written for the weights of the boxes based on the relationships given in the problem statement. One equation will be for the total weight of 1 large and 1 small box; the other will be for the total weight of 70 large and 60 small boxes.

Let L and S represent the weights of Large and Small boxes, respectively. The system of equations is ...

L + S = 60 . . . . . . combined weight is 60 lbs

70L +60S = 4000 . . . . weight of boxes in the truck

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We can solve this by substituting for s in the second equation.

70L +60(60 -L) = 4000

10L = 400 . . . . . . . . . subtract 3600, simplify

L = 40

S = 60 -L = 20

A large box weighs 40 pounds; a small box weighs 20 pounds.