The rule
a × b = c × x, so x = (a × b) ÷ c
Why it works
In an inverse proportion the product of the paired values never changes. Double one and the other halves, so the product survives untouched — and that constant is what lets you solve for the missing value.
How to do it by hand
- Multiply the first pair to get the constant
- Divide it by the third value
- That is the missing value
- Check: the new pair should multiply to the same constant
What is worth knowing
Inverse proportions are everywhere once you look: speed and travel time, workers and days, pressure and volume at fixed temperature. The last is Boyle's law, which is exactly this relationship with a name. The trap is assuming a relationship is inverse just because the quantities move oppositely — they also have to move in exact step. Doubling the workers rarely halves the time in practice, because communication overhead grows, which is Brooks's law and the reason the model is an idealisation.