Question

A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes weigh 30 pounds each. There are 120 boxes in all. If the truck is carrying a total of 4900 pounds in boxes, how many of each type of box is it carrying?A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes weigh 30 pounds each. There are 120 boxes in all. If the truck is carrying a total of 4900 pounds in boxes, how many of each type of box is it carrying?

Answer 1

55 small boxes, 65 large boxes.

Explanation:

First, we let x = the amount of big boxes and let y = the amount small boxes. Then, we know that any combination of such will equal 120 so we say

x + y = 120

We also know that we have to fill 4900 pounds, so we can say

50x + 30y = 4900

Then, we can use either substitution or elimination. I'll do substitution. we make the first equation

x = 120 - y

And now we can plug this into our second equation

50(120 - y) + 30y = 4900

Then we distrubute

6000 - 50y + 30y = 4900

Then simplify

6000 - 20y = 4900

Subtract 6000 from both sides

-20y = -1100

then divide both sides by -20

y = 55

so there are 55 small boxes, which means we can subtract 55 from 120 to get 65 large boxes.