ABSTRACT We analyse VLT/X-shooter data for seven quasars, where we study the relationships between their broad absorption line (BAL) and emission line outflows. We find (1) the luminosity of the [O iii] λ5007 emission profile decreases with increasing electron number density ($n_\mathrm{e}$) derived from the BAL outflow in the same quasar, (2) the measured velocity widths from the [O iii] emission features and C iv absorption troughs in the same object are similar, and (3) the mean radial velocity derived from the BAL outflow is moderately larger than the one from the [O iii] emission outflow. These findings are consistent with [O iii] and BAL outflows being different manifestations of the same wind, and the observed relationships are likely a reflection of the outflow density distribution. When we have outflows with smaller distances to the central source, their $n_\mathrm{e}$ is higher. Therefore, the [O iii] emission is collisionally de-excited and the [O iii] luminosity is then suppressed. Comparisons to previous studies show that the objects in our sample exhibit broad [O iii] emission features similar to the ones in extremely red quasars (ERQs). This might imply that BAL quasars and ERQs have the same geometry of outflows or are at a similar evolutionary stage. We find that the physical parameters derived from the BAL outflows can explain the amount of observed [O iii] luminosity, which strengthens our claim that both BAL and [O iii] outflows are from the same wind. These estimates can be tested with upcoming James Webb Space Telescope, which will be able to spatially resolve some of the ionized gas outflows.