In those counties without juvenile detention homes, if the district judges of such counties shall determine it advisable that a juvenile within such counties should be transferred to a juvenile detention home for safekeeping or detention, and the board of county commissioners of the county in which the juvenile detention home is located agree [agrees] to said transfer, the county from which said juvenile is transferred shall bear the expense of the maintenance and upkeep of said juvenile in the juvenile detention home, which upkeep and maintenance of such juvenile shall be the sum computed by adding the actual per diem cost of housing said juvenile to an amount equal to fifty percent of such per diem housing cost to cover administrative and amortization expense.