Science of Metabolism

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I'm a HS science teacher and this module we are talking about diet and metabolism, including eating disorders. Last year some smartass kid tried correcting one of my exam questions. My example was an anorexic girl who weighed 85 pounds - calculate her todal daily energy expenditure. Well the kid said that the anorexic girl would have a lower TDEE because of a slowed metablism and that whatever equation I was teaching them was wrong. The whole class laughed at me and all the girls who used to flirt with me shunned me thereafter.
So I'm trying to avoid the same mistake this year.
Can anyone help scientifically and mathematically model the TDEE of an anorexic woman?
pic obviously related