How much does a bottle of wine weigh if it is 1 kg plus half its own weight?

Half of the bottle's weight plus 1 kg = bottle's weight

0.5n + 1 = n

1 = 0.5n

2 = n

I have a different answer than those above that don't make a whole lot of sense. I believe the answer deals with asymptotes. If a bottle of wine is 1kg, plus half its own weight then it is 1.5kg. Since that added 0.5kg is part of the weight of the bottle of wine, you have to take that into account and add half of 0.5kg, which is 1.75kg. Since that added 0.25kg wasn't taken into consideration and is part of the weight of the bottle, you must add half of that to the mix which is 0.125kg for a total of 1.875kg. This process continues on and on to infinity.

1 + 1/2 + 1/4 +1/8 + 1/16 ... 1/n = 2kg

The truth is, the number will never reach 2kg. The best way to explain it is that when you go half way between 1 and 2, you get 1.5. When you go another half way, you get 1.75. You keep going halfway to infinity and will never reach 2. The number 2 in this problem would be called an asymptote.

If you check the 1.5 kg answer, you will discover that it does not work: half of that, plus 1 kg, is 1.75 kg, not 1.5. Two kilos is correct. Algebra: W = 1 + W/2; W/2 = 1; W = 2.

they don't tell you the weight. the 1 kg could be added to anything, as long it was half the weight of the bottle. 2 kg works b/c 1 plus half of 2 equals 2. it is the only # that works.

It's 2 kg.

If it's weight is equal to half its weight plus 1 kg, then 1 kg must be the other half of its weight, so to speak.

The math in it:

If you let x = the weight of bottle of wine, then...

0.5x + 1 = x

0.5x = 1

x = 2 kg

Hope that helped.

weight = 1 + 1/2 weight

weight - 1/2 weight = 1

so 1/2 weight = 1 and weight must = 2

1kg must weigh the other half so the whole bottle weighs 2kg.

ok sapphires answer was the one that made sense..

but then i re-read the question and im still baffled.

if it weighs 1kg thats its own weight. so half of that weight is 0.5kg.

so i stil come out with 1.5 kg.

but but but... it doesnt say where that 1kg came frm if you get me haha.

i still say its 1.5kg.

stick with ur instincts! who needs maths like this?!

well if its, 1kg + half of its weight, then logically two halves make a whole. so 1kg would have to be half of its weight. thus, the bottle weighs 2kg

Let w=the weight of the bottle of wine.

therefore;

w=1kg+0.5w ie 1kg+half of its weight.

w-0.5w=1kg

0.5w=1kg

w=1/0.5

w=2kg