The number of muons produced in extensive air showers is a reliable proxy for the amount of hadron production that occurs during the shower development. It is, therefore, an important observable in the context of identifying the mass composition of ultrahigh-energy cosmic rays. Beyond LHC energies, however, hadronic multiparticle production as it occurs in air showers from ultrahigh-energy cosmic rays, is poorly understood, and currently there is little to no way to directly test it experimentally. In simulations, current models of hadronic interactions are unable to produce the average number of muons that is measured by multiple air-shower experiments. In this work, we estimate the number of muons in vertical hybrid events detected by both the fluorescence and surface detectors of the Pierre Auger Observatory above a primary energy of 3 EeV. To reconstruct the signal, we use a model of the water-Cherenkov detector responses that is based on air-shower universality. We take into account the effect of the longitudinal shower development on the lateral distribution of the signal at the ground, as well as the primary energy estimated from the calorimetric energy deposition of the air shower. In this way, we are able to estimate the amount of muons created in vertical showers, relative to expectations from simulated showers using modern hadronic interaction models.