Using a sample of 471 million B{bar B} events collected with the BABAR detector, we study the sum of seven exclusive final states B {yields} X{sub s(d){gamma}}, where X{sub s(d)} is a strange (non-strange) hadronic system with a mass of up to 2.0 GeV/c{sup 2}. After correcting for unobserved decay modes, we obtain a branching fraction for b {yields} d{gamma} of (9.2 {+-} 2.0(stat.) {+-} 2.3(syst.)) x 10{sup -6} in this mass range, and a branching fraction for b {yields} s{gamma} of (23.0 {+-} 0.8(stat.) {+-} 3.0(syst.)) x 10{sup -5} in the same mass range. We find {Beta}(b{yields}d{gamma})/{Beta}(b{yields}s{gamma}) = 0.040 {+-} 0.009(stat.) {+-} 0.010(syst.), from which we determine |V{sub td}/V{sub ts}| = 0.199 {+-} 0.022(stat.) {+-} 0.024(syst.) {+-} 0.002(th.).