You have 100kg of Martian potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water. How much do they weigh now?
Logic:
Initially the non-water weight is 1kg, which is 1% of 100kg. After dehydration, 1kg is 2% of how many kilograms? In order that that percentage be twice as big, the total weight must be half as big. Therefore the weight is 50kg.
Algebra:
The weight of water in the fresh potatoes is 99% of 100 kg = 99kg
Let x be the weight of water lost when they dehydrate (i.e. x kg of water is lost)
So the final result is (99 – x) kg water
However, the final result can also be expressed as (100 – x) kg of potatoes which contain 98% water, that is 0.98 (100 – x) kg water
Equating
(99 – x) = 0.98 (100 – x)
99 – x = 98 – 0.98x
1 = 0.02x
x = 50
therefore 50 kg of water is lost and the potatoes weigh 50kg
