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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?

Respuesta :

carlosego
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
Ver imagen carlosego
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

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