Pursuant to an agreement authorized by RCW 35.77.020, the board of county commissioners may expend funds from the county road fund for the construction, repair, and maintenance of the streets of such city or town and for engineering and administrative services. Payments by a city or town under such an agreement shall be made to the county treasurer and by him or her deposited in the county road fund. Such construction, repair, maintenance, and engineering service shall be ordered by resolution and proceedings conducted in respect thereto in the same manner as provided for the construction, repair, and maintenance of county roads by counties, and for the preparation of maps, plans and specifications, advertising and award of contracts therefor: PROVIDED, That except in case of emergency all construction work performed by a county on city streets pursuant to RCW 35.77.020 through 35.77.040, which exceeds ten thousand dollars, shall be done by contract, unless after advertisement and solicitation of competitive bids it appears that bids are unobtainable or that the lowest bid exceeds the amount for which such construction can be done by means other than contract. No street construction project shall be divided into lesser component parts for the purpose of avoiding the requirements for competitive bidding.