Drying potatoes
You have 100 kg of potatoes that are 99% water by weight. You let them dry until they are 98% water.
What do they weigh now, in kg?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
The dry matter does not change while the potatoes dry.
How much dry matter is there, and what share of the new weight is it?
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Only water evaporates, so the dry matter stays at 1 kg. It was 1% of the weight and is now 2%, so the total weight has halved.
Step 1. The potatoes contain kg of dry matter.
Step 2. After drying, that 1 kg is of the total. So the total is kg.
The trap. “One percentage point less water” suggests losing about 1 kg. But the share of dry matter doubled, from 1% to 2%, so the weight is halved: 50 kg of water evaporated.