**How many Calories does it provide?**

The aim of this article is to find the **fuel value** and **calories** of a given serving of **M&M candies**.

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.

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

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

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

## Expert Answer

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 f**uel 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:

\[Total\ Fuel\ Value\ Per\ Pound=Fat+Carbohydrate+Protien\]

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

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