Grade 10 Math · The better buy
The number that makes tags honest
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The number that makes tags honest

Two bags, two sizes, two prices — which one is the deal? The tags can't be compared as they stand, so you give each one the same haircut: p=Cmp = \dfrac{C}{m} (read aloud: p equals C over m). The unit price pp is the Cost of the bag shared over the Mass inside it, in dollars per kilogram. Once both bags speak $/kg, the smaller number simply wins — bag size stops mattering, which was the whole idea.

One shelf trick to watch for: some tags whisper the price per 100 g because the number looks tiny next to a per-kilogram tag. Same rate, different clothes — multiply a per-100-g price by ten before letting it race a per-kilogram one. Units guide you here; make them match before you compare.