Gulnora runs a tea shop in the old bazaar of Samarkand. She sells two green teas: an everyday tea from Fergana at 6 dollars a kilogram and a fine tea from China at 12 dollars a kilogram.
One morning the manager of a large hotel came in with an order. He needed 60 kilograms of tea for the season and had a firm budget: he wanted a blend that costs 8 dollars a kilogram, better than the everyday tea but cheaper than the fine one.
Gulnora did not reach for a calculator. Eight dollars is 2 dollars above the cheap tea and 4 dollars below the fine tea. The blend must lean toward the cheaper tea, she reasoned, because 8 is closer to 6 than to 12. So she swapped the distances: the cheap tea gets the larger one, 4, and the fine tea gets the smaller one, 2. She would mix them in the ratio 2 to 1.
Sixty kilograms split in the ratio 2 to 1 is 40 kilograms of everyday tea and 20 kilograms of fine tea. She checked it the long way. Forty kilograms at 6 dollars cost 240 dollars, and twenty kilograms at 12 dollars cost another 240. That is 480 dollars for 60 kilograms, exactly 8 dollars a kilogram.
The hotel manager tasted a cup and signed the order. Gulnora wrote the blend's recipe on the back of a receipt and pinned it above the scales. Two months later the hotel asked for the same blend again, and she did not have to work anything out at all.