How many large boxes, x, can the lift carry?

Question

a lift at a warehouse has a capacity of 500 pounds. small boxes weigh 10 pounds each, medium boxes weigh 15 pounds each, and large boxes weigh 25 pounds each. the lift is already carrying 8 small boxes and 4 medium boxes.

Answer 1

So since the lift has a capacity of 500 pounds, we're going to set up an inequality that sets up this situation. We're going to need an inequality instead of an equation, because theoretically, the lift could carry 0 large boxes and it would still be okay... but it could also carry even more. So there's no set amount that the lift *has* to carry.

First - remember that to find the total weight of each type of box, you're going to multiply the weight of each box times the number of boxes. So...

1. The total weight of the small boxes: (10)(8) = 80
2. The total weight of the medium boxes: (15)(4) = 60
3. The total weight of the large boxes: (25)(x) = 25x

So now we can set up our inequality:

80 + 60 + 25x ≤ 500

140 + 25x ≤ 500

25x ≤ 360

x ≤ 14.4

Since boxes can't be decimal answers, this means that the lift can carry up to 14 boxes. (Might also be written as the lift can carry at most 14 boxes.)

Hope this helps! Feel free to reach out to schedule more one-on-one support!