Tutoring math, you’re often asked about real-world uses of it.  Here’s an application we might all find useful now and again.

Recently it occurred to me to look up the calorie density of proteins, fats, and carbohydrates.  My reasoning was that peoples’ fear of fat must be motivated by a high calorie content.  Then again, I reflected, it’s sugary foods – desserts, for example –  that are often implicated as adding pounds.  Some people, though, suggest that red meat puts the weight on them.

Is there a particular culprit, or do the foods work in concert to fatten us up?  Well, courtesy of Wikipedia I can report the following calorie densities:

fats:                                                9 cal/g

carbohydrates (flour, sugar, etc):      4 cal/g

protein                                         :  4 cal/g

I decided to become my own calorie counter.  Selecting three foods, I read each food’s calorie count, then its grams of fat, carbohydrates, and protein.  Using the densities above, I calculated the food’s “theoretical” number of calories.  In each case it was spot on.

Food 1:

calories:  160 (reported on label)

fat:                     5g
carbohydrate:   27g
protein:              1g

To calculate the theoretical number of calories, we proceed as follows:

from fat:                     9cal/g x  5g =      45 cal
from carbohydrates:   4cal/g x 27g =    108 cal
from protein:              4cal/g x   1g =        4 cal
total calories:                                       157 cal

What do you know?  The difference between 157 and 160 – which is less than 2 % – is probably due to rounding.  For practical purposes, it’s an exact match.

Food 2:  the package said 5g of fat, 42g of carbohydrates, and 5g of protein.  It gave a calorie count of 230.  Here are my numbers:

from fat:                      9cal/g x 5g =     45 cal
from carbohydrates:    4cal/g x 42g =  168 cal
from protein:               4 cal/g x 5g =     20 cal
total calories:                                      233 cal

Once again, the package’s count is spot on.

Food 3:  The label says 8g fat, 3g carbohydrates, 4g protein, and 100 calories.  My calculation:

from fat:                     9cal/g x 8g =      72 cal
from carbohydrates:    4cal/g x 3g =     12 cal
from protein:               4cal/g x 4g =     16 cal
total calories:                                      100 cal

Our formulaic calorie count exactly matches the label.

You can use this fun method for predicting the calorie content of foods you make at home:)

Posted by Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.