The membership of a district library fell by 12% in 2022 and then rose by 25% in 2023, ending that year at 6,600 members. How many members did it have at the start of 2022?

If the starting membership was $M$, then $Mx0.88\times 1.25=6600$. Since $0.88\times 1.25=1.10,M=6600/1.10=6,000$. Check: 6000 -> 5280 -> 6600. 5,280 undoes only the 25% rise and 7,500 undoes only the 12% fall, each dropping one stage. 7,260 applies the net factor 1.10 forward instead of backward.