A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 60 pounds each, and the small boxes weigh 20 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4700 pounds in boxes, how many of each type of box is it carrying?

55 large boxes and 70 small boxes

Step-by-step explanation:

We understand that there are two unknowns in this problem: the number of large boxes and the number of small boxes.

Let's identify with the letter L the number of large boxes that are transported, and with the letter S the number of small boxes, so we can easily identify the unknowns when writing and reading our equations and final answers.

Set up two equations:

1) one for the total weight of the boxes being transported (which should add up to 4700 pounds), and considering that we have "L" number of large boxes (each one 60 pound weight), and "S" number of boxes (each one 20 pound weight):

60 * L + 20 * S = 4700

2) another equation for the total number of boxes (125) which should be addition of L large boxes and S small ones:

L + S = 125

Now solve for one of the unknowns (let's say for example "S") in the easy second equation we wrote:

S = 125 - L

Now use this expression for "S" (to replace it in terms of L) in the first (more complex) equation:

60 * L + 20 * (125-L) = 4700

Now apply distributive property to remove the parenthesis on the second term on the left of the equation:

60 * L + 2500 - 20 * L = 4700

subtract 2500 from both sides (to group all numerical terms on the right hand side):

60 * L - 20 * L = 4700-2500 = 2200

combine the like terms 60L and - 20L:

40 * L = 2200

now divide both sides by 40 to solve for L

therefore: L = 2200 / 40 = 55

There are 55 large boxes.

Now to find the number of small boxes, we use this result: "L=55" in the second (simple/easy) equation we created:

S = 125 - L = 70

Therefore, there are 70 small boxes.