Audio/visual recognition and retrieval applications have recently garnered significant attention within Internet-of-Things (IoT) oriented services, given that video cameras and audio processing chipsets are now ubiquitous even in low-end embedded systems. In the most typical scenario for such services, each device extracts audio/visual features and compacts them into feature descriptors, which comprise media queries. These queries are uploaded to a remote cloud computing service that performs content matching for classification or retrieval applications. Two of the most crucial aspects for such services are: $(i)$ controlling the device energy consumption when using the service; $(ii)$ reducing the billing cost incurred from the cloud infrastructure provider. In this paper we derive analytic conditions for the optimal coupling between the device energy consumption and the incurred cloud infrastructure billing. Our framework encapsulates: the energy consumption to produce and transmit audio/visual queries, the billing rates of the cloud infrastructure, the number of devices concurrently connected to the same cloud server, the query volume constraint of each cluster of devices, and the statistics of the query data production volume per device. Our analytic results are validated via a deployment with: $(i)$ the device side comprising compact image descriptors (queries) computed on Beaglebone Linux embedded platforms and transmitted to Amazon Web Services (AWS) Simple Storage Service; $(ii)$ the cloud side carrying out image similarity detection via AWS Elastic Compute Cloud (EC2) instances, with the AWS Auto Scaling being used to control the number of instances according to the demand.