Let’s say that freshly harvested cucumbers can have a water content of up to 99 percent. (Never mind that the U.S. Department of Agriculture gives the average figure as 96 percent.)
Last summer Farmer Braun accidentally left a box containing 10 kilograms of freshly harvested cucumbers outside in the blazing sun.
Over the course of a day, some of the water in the produce evaporated, and the water content fell from 99 percent to 98 percent.
When Farmer Braun put the cucumbers on a scale that evening, he was completely surprised when he looked at the display.
What was the new weight?
When the cucumbers dried out into the sun, their total mass went from 10 kilograms to just five. (It’s hard to believe, but it is possible.)
The 10 kg of cucumbers consisted of 99 percent water. The cucumbers therefore consisted of 9.9 kg of water and 0.1 kg of dry matter. (Recall that 99% of 10 = 0.99 × 10 and 1% of 10 = 0.01 × 10.)
In the figure below, each small square represents 1 percent.
Amanda Montañez
In the evening, the dry matter content was still 0.1 kg. Its share of the total mass increased to 2 percent, and the water content dropped to 98 percent.
In the figure below, each small square now represents 2 percent of the total mass after evaporation.
Amanda Montañez
If 2 percent of the cucumbers weighs exactly 0.1 kg, then 100 percent weighs exactly 50 times as much: 50 × 0.1 kg = 5 kg.
Alternately, this can be depicted with variables. Because 1 percent of the initial mass A corresponds to 2 percent of the reduced mass E after evaporation, the reduced mass equals half of the total mass:
0.01A = 0.02E ⟹ E = 0.01A⁄0.02 = 1⁄2A
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.