This is the boss. No calculator. Tonight the calcium factor is 2.5, the magnesium factor is 4, and the grains bridge is 17 mg/L per grain per gallon. Resin is rated at a flat 30,000 grains per cubic foot and the brine controller is set to 8 lb/ft³. Everything has been chosen to fit in your head.

One water, five lines, and every answer feeds the next: the two ion results become one hardness, the hardness crosses the bridge into grains per gallon, the grains meet the building's daily draw to make a load per day, the bed's capacity is divided by that load to give the run in days, and the run is held up against what the service contract promised. Write each line down as you go — one slip at the top rides all the way to the verdict.

And note what the last line asks for. It does not want another number; it wants a decision: does this bed keep the contract, yes or no. The arithmetic exists only to earn you the right to make it. Watch for the habit this chapter has been working against — a capacity in the tens of thousands of grains looks enormous right up until it is divided by what a building actually spends in a day.

A bonus mark follows, one line long. Some nights it is the salt order for the bed. Other nights it is the bypass blend at the taps, with the softened stream taken as zero: the grains per minute the bypass brings in, spread over the total flow.

Everything in the chapter rides in this one commissioning. 5★ under par here is the chapter crown. Clock in.