A sugar factory receives an order for 1000 units of sugar. The production manager thus orders production of 1000 units of sugar. He forgets, however, that the production of sugar requires some sugar (to prime the machines, for example), and so he ends up with only 900 units of sugar. He then orders an additional 100 units, and produces only 90 units. A further order for 10 units produces 9 units. Finally seeing he is wrong, the manager decides to try mathematics. He views the production process as an infinite geometric series with a₁ = 1000 and r = 0.1.
(a) Using this, find the number of units of sugar that he should have ordered originally.
(b) Afterwards, the manager realizes a much simpler solution to his problem. If x is the amount of sugar he orders, and he only gets 90% of what he orders, he should solve 0.9x = 1000. What is the solution?