Remember, there may be an error or two, but checking out a couple combinations, it seems to work. But as for finding individual calorie numbers for each item, we don’t have enough info (or at least I don’t think we do), but we can certainly make an educated guess using a little extra information from the internet.
Sorry, the first column, third item under dinner should be “370” I think, not “390.”
Anyhow, checking out the nutrition info available online, picking just the minimum calorie items, I’m getting 1430 calories total, not 1370. (250 for the McMuffin, 400 for the cold cut combo, 160 for the fruit and yogurt parfait, 100 for the ombre drink, 520 for the chili talapia.) So use those numbers as a baseline for each category and adjust using the chart above to get a ballpark estimate of what each item is tallying up as calorically. I know it’s not the exact question you’re asking (solving the equation mathematically), but I think this is the best we can do (well, we can tweak the numbers above a bit to get even closer, but we’re pretty close as is.)
When you only have two equations, the only way they can possibly be dependent is if one is a multiple of the other. But when you have more equations, more possibilities open up, because anything that is a sum of multiples of other equations is also dependent. For instance:
x = y+z
2x = 3y-z
4x = 5y+z
No one equation here is a multiple of any other. But I created the third equation by doubling the first equation and adding it to the second. That means that, so long as the first two equations are true, the third one will also always be true, and so it adds no new information. My solutions could be, for instance, (4,3,1), but they could also be (12,9,3).
So now I see I was smart enough to know I couldn’t do it but not smart enough to know it couldn’t be done, at least not without more info. But pulykamell’s solution was a thing that I was thinking about: ranking each category from highest to lowest and then. . . dumb math brain said, “Duh, I dunno what you should do next. Why doncha ask some smart people?”
And, to belabour the obvious, from your chart one can systematically enumerate dozens of ways to get a total of exactly 2000 calories (which gives a thumbs-down on the quiz, for some reason), and nearly as many ways of obtaining 1990 calories (e.g., 1370+30+70+260+80+180). Of course, Biggirl’s original question remains unsolvable for the reasons everyone has indicated.