Voters on Tuesday were approving a property-tax levy rate increase meant to boost the finances of Valley Medical Center.

The King County public hospital district’s Proposition No. 1 was passing with 55.7% in Tuesday night’s vote count. District officials have estimated the proposed increase would bring an additional $40 million a year to the Renton-based hospital. If approved, this would be the first time in 20 years voters have raised the levy rate.

The measure was on the ballot in the hospital district that takes in Kent, Renton, Tukwila, and parts of Auburn, Black Diamond, Covington, Federal Way, Maple Valley, Newcastle and Seattle.

The change would cost homeowners 75 cents — or 46 cents more — for every $1,000 of assessed property value. A home assessed at $700,000, for example, wou

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