Question

How many of each type of box is it carrying?

Answer 1

Number of large boxes = 55

Number of small boxes = 65

Explanation:

We know that large boxes weight 60 pounds each while small boxes weight 30 pounds each and they are 120 boxes in total which weigh 5250 pounds in total.

Assuming
`l` to the number of large boxes and
`s` to be the number of small boxes, we can write the following equations:

`l+s=120` --- (1)

`60l+30s=5250` --- (2)

From equation (1):

`l=120-s`

Substituting this value of
`l` in (2):

`60(120-s)+30s=5250`

`7200-60s+30s=5250`

`60s-30s=7200-5250`

`30s=1950`

s = 65

Now finding the value of
`s`:

`l=120-65`

l = 55

Therefore, number of large boxes = 55 and number of small boxes = 65.

Answer 2

Number of large boxes: 55

Number of small boxes:65

Explanation:

Let be "l" the number of large boxes and "s" the number of small boxes.

Set up a system of equations:

`\left \{ {{l+s=120} \atop {60l+30s=5250}} \right.`

Use the methof of elimination. Mulitply the first equation by -60 and add both equations. Then solve for "s":

`\left \{ {{-60l-60s=-7200} \atop {60l+30s=5250}} \right.\\.........................\\-30s=-1950\\s=65`

Substitute s=65 into any of the original equations and solve for "l":

`l+65=120\\l=55`