Wash. Rev. Code § 35.58.420
Each component city shall pay such proportion of the supplemental income of the metropolitan municipal corporation as the assessed valuation of property within its limits bears to the total assessed valuation of taxable property within the metropolitan area. Each component county shall pay such proportion of such supplemental income as the assessed valuation of the property within the unincorporated area of such county lying within the metropolitan area bears to the total assessed valuation of taxable property within the metropolitan area. In making such determination, the metropolitan council shall use the last available assessed valuations. The metropolitan council shall certify to each component city and county, prior to the fourth Monday in June of each year, the share of the supplemental income to be paid by such component city or county for the next calendar year. The latter shall then include such amount in its budget for the ensuing calendar year, and during such year shall pay to the metropolitan municipal corporation, in equal quarterly installments, the amount of its supplemental income share from whatever sources may be available to it.
RCW 35.58.420