We describe the B-0 and B-s(0) decays into J/psi f(0)(500) and J/psi f(0)(980) by taking into account the dominant process for the weak decay of B-0 and B-s(0) into J/psi and a q (q) over bar component. After hadronization of this q (q) over bar component into pairs of pseudoscalar mesons we obtain certain weights for the meson-meson components and allow them to interact among themselves. The final state interaction of the meson-meson components, described in terms of chiral unitary theory, gives rise to the f(0)(980) and f(0)(500) resonances and we can obtain the pi(+)pi(-) invariant mass distributions after the decay of the resonances, which allows us to compare directly to the experiments. We obtain ratios of J/psi f(0)(980) and J/psi f(0)( 500) for each of the B decays in quantitative agreement with experiment, with the f(0)(980) clearly dominant in the B-s(0) decay and the f(0)(500) in the B-0 decay.