Taking as bioinspiration the remarkable acoustic absorption properties of moth wings, we develop a simple analytical model that describes the interaction between acoustic pressure fields, and thin elastic plates incorporating resonant sub-structures. The moth wing is an exemplar of a natural acoustic metamaterial; the wings are deeply subwavelength in thickness at the frequencies of interest, the absorption is broadband and the tiny scales resonate on the moth wing acting in concert. The simplified model incorporates only the essential physics and the scales are idealized to flat rigid rectangular plates coupled via a spring to an elastic plate that forms the wing; all the components are deep-subwavelength at desired frequencies. Based on Fourier analysis, complemented by phenomenological modelling, our theory shows excellent agreement with simulation mimicking the moth-wing structure. Moth wings operate as broadband sound absorbers employing a range of scale sizes. We demonstrate that a random distribution of scale sizes generates a broadband absorption spectrum. To further illustrate the potential of the model, we design a deeply sub-wavelength acoustic counterpart of electromagnetically induced reflectance.