Can you help me solve this?

Question

Suppose you have a bunch of wooden beds, each weighing 200 pounds each, arranged in a pyramid. The base layer is 5 beds by 5 beds, the layer above is 4 beds by 4 beds, and so on until the top layer of one bed. They are arranged in such a way that each bed is resting on four beds below it, one leg on each bed.

If the weight on each bed is always equally distributed to all four legs, and each bed leg can only support 200 pounds, how many pounds can you place on top of the topmost bed? Please round to the nearest pound

Answer 1

200 pounds..

Answer 2

200

lbs

Answer 3

Each bed leg can support 200 pounds. Therefore each bed can support 800 pounds. Each bed weighs 200 pounds so each bed leg is supporting 50 pounds with no other bed on top of it.

When you put on the 2nd level of 16 beds you are adding 12.5 pounds to each of the bed legs on the bottom level so that each of the bed legs on the 1st level are now holding 62.5 pounds. rounding up makes it 63 pounds per bed leg.

The 3rd level of 9 beds adds 3.125 per leg, rounded off makes it 3 more pounds, making it 66 pounds per leg.

The 4th level of 4 beds adds .78125 pounds per leg, rounded makes it 1 pound per leg which makes it 67 pounds per leg total.

The top layer of 1 bed only adds .195125 pounds per leg on the bottom layer which isn't significant enough to matter.

Since each leg on the bottom level is now supporting 67 pounds and is capable of supporting 200 lbs. that means each leg on the bottom layer can support another 133 lbs.

You can place 600 lbs on the top bed. That would make the top bed weigh 800 lbs. (600 + 200 lbs per bed).

800/4 = 200 lbs on each leg which equals 200 lbs on each bed in the next level.

200 lbs divided by 4 = 50 lbs. per leg on each bed in the next level

50 lbs divided by 4 = 12.5 lbs. on each bed on the next level.

Which only puts 3.125 lbs on each bed on the bottom level.

So the most weight you can PLACE ON TOP of the very top bed is 600 lbs.

Answer 4

800 lbs

Answer 5

I think its 200 pounds aproximately.

Answer 6

800