Where the courts of quarter sessions of the peace of any county within this Commonwealth heretofore have or hereafter may sentence and commit children or minors, under the various juvenile court acts of this Commonwealth, to homes or institutions without this Commonwealth, in every such case such county, from which such child or minor has been or shall be so sentenced, shall be liable for a reasonable charge for such maintenance, when the amount is ascertained and approved as hereinafter provided for.
11 P.S. § 148