# A pound of plain M&M candies contains 96g fat, 320g carbohydrate, and 21g protein. What is the fuel value in kJ in a 42g (about 1.5-oz) serving?

How many Calories does it provide?

The basic concept behind this article is the Atwater System and the average values of energy supplied by macronutrients of food such as carbohydrates, fat, protein, and fiber.

The Atwater System is a standardized method to calculate the total calorific value of the given amount of food by considering factors related to the energy conversion of macronutrients like carbohydrates, fat, protein, and fiber which are present in the food.

The Atwater system expresses the average standard calorific value or fuel value of macronutrients in terms of calories per gram of those nutrients.

$1g\ of\ Protein\ =\ 17\frac{kJ}{g}\ =\ 4\frac{kcal}{g}$

$1g\ of\ Carbohydrate\ =\ 17\frac{kJ}{g}\ =\ 4\frac{kcal}{g}$

$1g\ of\ Fat\ =\ 38\frac{kJ}{g}\ =\ 9\frac{kcal}{g}$

Given that:

M&M Candies Serving Mass = 42g

A pound of M&M Candies contains the following macronutrients:

Fat $=\ 96g$

Carbohydrate $=\ 320g$

Protein $=\ 21g$

Part-A

For the given serving, we will calculate the fuel value per pound of M&M candies.

The standard fuel value for Fat is:

$1g\ of\ Fat=38\frac{kJ}{g}$

$96g\ of\ Fat=38\frac{kJ}{g}\times96g$

$96g\ of\ Fat=3648\ kJ$

The standard fuel value for Carbohydrate is:

$1g\ of\ Carbohydrate=17\frac{kJ}{g}$

$320g\ of\ Carbohydrate=17\frac{kJ}{g}\times320g$

$320g\ of\ Carbohydrate=5440kJ$

The standard fuel value for Protein is:

$1g\ of\ Protein=17\frac{kJ}{g}$

$21g\ of\ Protein=17\frac{kJ}{g}\times21g$

$21\ g\ of\ Protein=357\ kJ$

So, to calculate the total fuel value per pound of M&Ms, we will sum the individual energy or fuel values of its macronutrients as follows:

$Total\ Fuel\ Value\ Per\ Pound=Fat+Carbohydrate+Protien$

$Total\ Fuel\ Value\ Per\ Pound=3648kJ+5440kJ+357kJ$

$Total\ Fuel\ Value\ Per\ Pound=9445\frac{kJ}{lb}$

Now, we will calculate the fuel value per gram of M&M as per below relation:

$Total\ Fuel\ Value\ Per\ Gram=Total\ Fuel\ Value\ Per\ Pound\times\frac{1lb}{453.6g}$

$Total\ Fuel\ Value\ Per\ Gram=9445\frac{kJ}{lb}\times\frac{1lb}{453.6g}$

$Total\ Fuel\ Value\ Per\ Gram=9445\frac{kJ}{lb}\times\frac{1lb}{453.6g}$

$Total\ Fuel\ Value\ Per\ Gram=20.822\frac{kJ}{g}$

Finally, to calculate the fuel value of 42-g (about 1.5 oz) of M&M serving:

$Fuel\ Value\ Per\ Serving=Total\ Fuel\ Value\ Per\ Gram\times Mass\ of\ Serving$

$Fuel\ Value\ Per\ Serving\ (42g)=20.822\frac{kJ}{g}\times42g$

$Fuel\ Value\ Per\ Serving\ (42g)=874.524kJ$

Part-B

To calculate the calories given by a given serving of M&M, we will use the following relation:

$1kJ=0.239kCal$

By using the unitary method, we will convert the Fuel Value per serving into Calories:

$874.524kJ=874.524\times0.239kcal$

Hence:

$Calories\ Per\ Serving\ (42g)=874.524kJ=209.01kcal$

## Numerical Result

Fuel value in kJ in a 42g serving of M&M is $=\ 874.524kJ$.

Calories in 42g serving of M&M is $=\ 209.01kcal$.

## Example

A pound of pastry contains 50 g fat, 250 g carbohydrate, and 30 g protein. What is the fuel value in kJ per pound of serving?

Solution

The standard fuel value for Fat is:

$1g\ of\ Fat=38\frac{kJ}{g}$

$50g\ of\ Fat=1900\ kJ$

The standard fuel value for Carbohydrate is:

$1g\ of\ Carbohydrate=17\frac{kJ}{g}$

$250g\ of\ Carbohydrate=4250kJ$

The standard fuel value for Protein is:

$1g\ of\ Protein=17\frac{kJ}{g}$

$30\ g\ of\ Protein=510\ kJ$

So, the total fuel value per pound of pastry is:

$Total\ Fuel\ Value\ Per\ Pound=Fat+Carbohydrate+Protien$

$Total\ Fuel\ Value\ Per\ Pound=1900kJ+4250kJ+510kJ$

$Total\ Fuel\ Value\ Per\ Pound=6660\frac{kJ}{lb}$