Final answer:
The first true adding machine referred to in this context was invented in 1885, contributing significantly to office productivity in the late 19th century alongside the typewriter and cash register.
Step-by-step explanation:
The inventor of the first true adding machine was Blaise Pascal, who in 1642 created a mechanical calculator capable of performing additions and subtractions directly and carrying tens to the next column. However, in the context of the provided information, the adding machine referred to was invented in 1885, which aligns with the invention of William Seward Burroughs' adding machine. This device became a crucial part of office productivity and is one of the early predecessors to the modern computer.
The adding machine, along with other office productivity tools like the typewriter and the cash register, greatly enhanced worker productivity in the late 19th century. While the typewriter was invented in 1867 and the cash register in 1879, it was the adding machine in the 1880s that completed the trio, enabling businesses to keep up with the ever-growing demands of the bustling economy during the Industrial Revolution.