Question

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?

Answer 1

we have 60 large boxes and 50 small boxes.

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.

Answer 2

9514 1404 393

Answer:

• 45# -- 60 boxes
• 30# -- 50 boxes

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.