I ran into this question today:
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t = n + 2, how many additional tea bags are needed to make each additional cup of tea?
The answer is 1. For example, if I want to make n cups of tea, but then decide to make n + 1 cups instead, I'll need n + 3 teabags instead of n + 2 teabags. In other words, the change in t for a 1-unit increase in n is 1 (which we can gather from the slope in the given linear equation).
But wait. Is there a valid alternative interpretation such that the answer is 3? Suppose, as the prompt states, n cups of tea are made by adding t tea bags to hot water. Those cups are sold and gone. Five minutes later, an additional cup of tea is ordered. This will require 3 additional tea bags on top of the t tea bags used earlier.
Is the alternative interpretation obviously wrong? If so, why?
Yes and no it is wrong. This is less of a mathematical problem than an english one. It all depends how you define 'hot water'. In your alternate case in which the answer is '3' (We'll call this A and the other B) we refer to hot water as ambiguous in quantity i.e the statement still applies if their is more than one pot of water. In case B the pot of water is itself a single object. You can add to it but it is never gone. I.E the water never actually leaves the pot or in case A, gets 'sold and gone'. This is just a poorly written question. It's not even as kind as to say a or the hot water.