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 70 pounds. The truck is transporting 60 large boxes and 55 small boxes. If the truck is carrying a total of 4050 pounds in boxes, how much does each type of box weigh?

Answer 1

the large boxes weigh 40 pounds and the smaller boxes weigh 30 pounds

Explanation:

define variables:

b is the weight of large boxes and s is the weight of small boxes. you can create two equations to represent what you know:

b + s = 70 (the weight of one large box and one small box is 70 pounds)

60b+ 55s = 4050 (the total weight of the 60 large boxes and the 55 small boxes is 4050)

then by making one of the equations equal to a variable, you can use substitution to solve.

s = 70 - b

so 60b + 55s = 4050 now becomes:

60b + 55(70 - b) = 4050, and next you solve for b

60b + 3850 - 55b = 4050

5b = 200

b = 40.

now you know that the large boxes weigh 40 pounds. to solve for the small box weight, you plug in b in either equation. i am going to choose the first once since it's fewer steps

b + s = 70 -> 40 + s = 70

s = 30

and now you know that the smaller boxes weigh 30 pounds.