While photoacoustic methods offer significant promise for high-resolution optical contrast imaging, quantification has thus far proved challenging. In this paper, a noniterative reconstruction technique for producing quantitative photoacoustic images of both absorption and scattering perturbations is introduced for the case when the optical properties of the turbid background are known and multiple optical illumination locations are used. Through theoretical developments and computational examples, it is demonstrated that multiple-illumination photoacoustic tomography (MI-PAT) can alleviate ill-posedness due to absorption-scattering nonuniqueness and produce quantitative high-resolution reconstructions of optical absorption, scattering, and Gruneisen parameter distributions. While numerical challenges still exist, we show that the linearized MI-PAT framework that we propose has orders of magnitude improved condition number compared with CW diffuse optical tomography.