I Uncovering the Mystery of Calorie Constants

[barryj]

When calculating calories of a food..
It is sort of well known that carbs have 4 cal/gram, protein has 4 cal/gram and fat has 9 cal/gram. I wanted to do an experiment to determine these constants 4,4,and 9

I looked at soup, peanut butter, and a protein mix to get the values from the labels per serving and the data is...

soup carb 13, prot 2, fat 2, calories 80 (78)
p butter carb 8, prot 7, fat 15, calories 190 (195)
mix carb 18, prot 2, fat 4, calories 110 (116)

Note: numbers in ( ) are calculated from the 4,4,9 values. These numbers are reasonably close to what was listed on the label

so I set up a matrix where a= cal/gram for carb, b = cal/gram for prot, and c = cal/gram for fat
The matrix is..

13a + 2b + 2c = 80
8a +7b +15c = 190
18a + 2b + 4c = 110

Solving I got a = 3.65, b = 10.391 really?, and c = 5.85 ?really.

My calculated values are not even close to what I expected, around 4,4,9

Does anybody know why this is?? I am really puzzled.

 

[Mark44]

so I set up a matrix where a= cal/gram for carb, b = cal/gram for prot, and c = cal/gram for fat
The matrix is..

13a + 2b + 2c = 80
8a +7b +15c = 190
18a + 2b + 4c = 110

Solving I got a = 3.65, b = 10.391 really?, and c = 5.85 ?really.

My calculated values are not even close to what I expected, around 4,4,9

In your matrix calculation, if you use the numbers you showed in parentheses (78, 195, 116), it comes out exactly as you would expect. This shouldn't be a surprise, as you used the values 4, 4, and 9 for the cal/g for carbs, protein, and fats. The seemingly relatively small change from (80, 190, 110) to (78, 195, 116) makes a fairly significant change in the solution, most notably on the value of your b variable (cal/g for protein).
Geometrically, you are working with three planes in space, and determining the point they have in common. By changing all three equations, even relatively slightly, you are changing the intersection point.