Writing Equations In Terms Of Variables I recently had a dispute over a lost mark with my maths teacher, and I'm seeking external clarification on the matter.
We were working with a graph showing the relationship between people's weights and the number of exercise hours they do in a week.
The question asked me to find the equation in terms of the two variables.
This was my answer (marked wrong):
Let W = Weight of a person in kg
Let E = The number of exercise hours undertaken each week by a person.

This is the answer my maths teacher claims is correct:

Surely not? Assuming both equations are correct (that wasn't the dispute), is my answer actually an incorrect response to the question? Are they both right? I actually think mine is better, having worded variables is illogical and belongs in programming not mathematics.
 A: IF you clearly defined your variables and their units, as you did in this post, in addition to providing your equation, I personally find your instructor's response pedantic, unless the instructions clearly asked you to represent the variables as "Weight" and as "Exercise". And I personally find the clear definitions (including units) as more informative than the alternative.
I don't think having "worded variables* is "illogical"; less than optimal, perhaps. But in all fairness,  "worded variables" in an equation can quickly convey the relationship(s) between variables, particularly alongside a graph, if the corresponding defined variables are buried in a footnote, or in the exposition itself.
A: What did your teacher say was the reason?
There's nothing inherently worse about having words as variable names in mathematics.  In fact, sometimes it's preferable, so the reader doesn't have to flick back asking Oh, what did $\chi$ mean again?.  It's common to use symbols mostly for reasons of consistency and succinctness.
With the information presented in the question, the equations appear essentially the same, up to presentation issues.  However, it's impossible to give an informed appraisal without seeing the full picture.
A: I'd say your answer is straightforwardly correct and the teacher's answer is not.
You are (coherently) equating two numbers -- one number measuring a weight, another number the output for the function $-1.27E + 57.46$ for argument $E$, the number measuring hours of exercise. So the two sides of your equation refer to the same type of thing.
Your teacher appears to be (incoherently) trying to equate a weight (one physical quantity) with ... well, with what? What does the right-hand side refer to? An hour of exercise is a period of time, as is 1.27 times as much time. How do we subtract a period of time from a number? That seems to be a dimensional mish-mash. And whatever we get, it won't be a quantity of weight. Of course, being charitable, that isn't what your teacher really meant -- S/he meant (let's hope!) what you correctly wrote!
