A delivery truck is transporting boxes of two sizes : large and small. The large boxes weigh 45 pounds each, and the small boxes weight 30 pounds each. There are 110 boxes in all. If the truck is carrying a total of 4200 pounds on boxes how many of each type of box is it carrying?

we have 60 large boxes and 50 small boxes.

Step-by-step explanation:

First, "boxes of two sizes" means we can assign variables:

  Let x = number of large boxes

       y = number of small boxes

Now, "There are 110 boxes in all"    means    x + y = 110

Now, the pounds for each kind of box is:

    (pounds per box)*(number of boxes)

pounds for large boxes     +    pounds for small boxes      =    4200pounds

                 "the truck is carrying a total of 4200 pounds in boxes"

        (45)*(x)                   +              (30)*(y)                  = 4200

Now, Solve for one of the variables in the first equation then replace (substitute) the expression for that variable in the second.  Let's solve for x:

   x = 110 - y          [from eq1]

    45(110-y) + 30y = 4200            [from eq2]

     4950 - 45y  + 30y= 4200         [distribute]

     4950 - 15y = 4200

      -15y = -750

         y = 50           [divide both sides by (-15)]

 There are 50 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

  x = 110 - y

  x = 110 - 50

  x = 60

 There are 60 large boxes.

Now, let's verify our solution:

Is   60+50= 110 ?       [eq1]

         110 = 110 ? yes!

Is  60(45) + 50(30) = 4125   ?

     2700 + 1500 = 4200 ?

       4200 = 4200 ? yes

So we have 60 large boxes and 50 small boxes.

9514 1404 393

Step-by-step explanation:

Let b represent the number of big boxes. Then 110-b is the number of small boxes. The total weight is ...

  30(110-b) +45b = 4200

  15b = 900 . . . . . . . . . . . . . subtract 3300

  b = 60 . . . . . . . . . . divide by 15

  110 -b = 110 -60 = 50 . . . number of small boxes

The truck is carrying 60 large boxes and 50 small boxes.

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