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Problem Pictures: Numbers - single user

Problem Pictures: Numbers

The third in the series continues the tradition of bringing mathematics to life with photographs using attractive, unusual and puzzling images.

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The potato paradox

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