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 95 pounds. the truck is transporting 50 large boxes and 65 small boxes. if the truck is carrying a total of 5275 pounds in boxes, how much does each type of box weigh?

Answer 1

Large box weighs 60 pounds while small box weighs 35 pounds.

Let x = large boxes and y = small boxes
We need two equations here:
50x + 65y = 5275
x + y = 95

Use x = 95 - y to and substitute x from the equation:
50(95 - y) + 65y = 5275
4750 - 50y + 65y = 5275
4750 + 15y = 5275
15y = 5275 - 4750
15y/15 = 525/15
y = 35

x + y = 95
x + 35 = 95
x = 60

To check:
50x + 65y = 5275 pounds
50(60) + 65(35) = 5275 pounds
3000 + 2275 = 5275 pounds

Answer 2

First we define the variables:
x = weight of a large box
y = weight of a small box
We write the system of equations:
x + y = 95
50x + 65y = 5275
The solution to the system of equations by the graphic method is:
x = 60
y = 35
Note: see attached image.
Answer:
each type of box weigh:
weight of a large box = 60 pounds
weight of a small box = 35 pounds