An architect drawing a small clinic had one number she did not yet have. The plot ran along a road whose width was still being argued about at the town hall, so the building's depth was, for the moment, simply «the unknown length».
She carried on anyway. The consulting room, she wrote, would have a floor area of three times that length plus twelve square metres. The waiting room would be five times the length plus five. Added together — and adding is nothing more than putting like with like — the two rooms come to eight times the length plus seventeen.
Then the corridor. It has to be taken out of the total, because it is not usable floor space: two times the length plus three. Subtracting means every part of that expression changes sign, so what remains is six times the length plus fourteen.
Three weeks later the town hall settled the road at a width that left the building six metres deep. She put six into her expression: six times six is thirty-six, plus fourteen, giving fifty square metres of usable floor.
She checked it the slow way as well. The consulting room came to thirty square metres, the waiting room to thirty-five, and the corridor took away fifteen — which is also fifty.
The point of the expression was never the answer. It was that the whole design could be finished, argued over and approved whatever the length turned out to be — and the arithmetic waited quietly at the end.