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Sveta_85 [38]
2 years ago
10

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?
Mathematics
2 answers:
ivolga24 [154]2 years ago
8 0

9514 1404 393

Answer:

  • 45# -- 60 boxes
  • 30# -- 50 boxes

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.

s344n2d4d5 [400]2 years ago
6 0

Answer:

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.

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Step-by-step explanation:

Hope that this helps you out! :)          

If you have any questions please put them in the comment section below this answer.          

Have a great rest of your day/night!          

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<h2>Evaluating Composite Functions</h2><h3>Answer:</h3>

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<h3>Step-by-step explanation:</h3>

We can write how w(f(m(x))) will be defined but that's too much work and it's only useful when we are evaluating w(f(m(x))) with many inputs.

First let's solve for m(2) first. As you read through this answer, you'll get the idea of what I'm doing.

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