Chapter 18, Problem 60E

Interpretation Introduction

Interpretation:

The percentage of calories obtained from fat is to be calculated.

Concept Introduction:

Fats and oils are composed of organic molecules called triglycerides. Triglycerides are the main sources of fats in the body.

Polyhydroxy aldehydes, or ketones and their derivatives, are called carbohydrates.

Fiber is the carbohydrate that contains more than two molecules or units of glucose linked by $\beta$-linkage.

The polymers of amino acids are called proteins.

Answer to Problem 60E

Solution:

a) $47\%$.

b) $12\%$.

c) $4.4\text{ \%}$

Explanation of Solution

a) In Vons tortilla chips,

Fats have a high calorific value, that is, up to $9\text{ Cal}/\text{g}$. Carbohydrates and proteins have calorific values equal to $4\text{ Cal}/\text{g}$ each. Fiber has almost nil or $0\text{ Cal}/\text{g}$ calorific value.

The number of calories in each product can be calculated as follows:

$\begin{array}{l}\underset{\_}{\begin{array}{c}\text{Fat }7\text{ g}\times \text{9 Cal}/\text{g}=\text{ 63 Cal}\\ \text{Protein }2\text{ g}\times 4\text{ Cal}/\text{g}=\text{ 8 Cal}\\ \text{Carbohydrate }16\text{ g}\times 4\text{ Cal}/\text{g}=64\text{ Cal }\end{array}}\\ \text{Total 135cal}\end{array}$

Thus, the total number of calories obtained is $\text{135cal}$.

The percentage of fats can be calculated as:

$\%\text{ of fats}=\frac{\text{Calories obtained from fats}}{\text{Calories obtained from the food}}\times 100$

Substitute $\text{63 Cal}$ for calories obtained from fats and $\text{135 Cal}$ for calories obtained from food in the above formula as follows:

$\begin{array}{c}\%\text{ of fats}=\frac{\text{63 Cal}}{\text{135 Cal}}\times 100\\ =0.466\times 100\\ =47\%\end{array}$

Therefore, the percentage of calories obtained from fatsis $47\%$.

b) In Nutri-gain cereal,

The number of calories in each product can be calculated as follows:

$\begin{array}{l}\underset{\_}{\begin{array}{c}\text{Fat 2 g}\times \text{9 Cal}/\text{g}=\text{ 18 Cal}\\ \text{Protein 3 g}\times 4\text{ Cal}/\text{g}=\text{ 12 Cal}\\ \text{Carbohydrate 31 g}\times 4\text{ Cal}/\text{g}=\text{ 12}4\text{ Cal }\end{array}}\\ \text{Total 154 cal}\end{array}$

Therefore, the total number of calories obtained is $154\text{ cal}$.

The percentage of fats can be calculated as follows:

$\%\text{ of fats}=\frac{\text{Calories obtained from fats}}{\text{Calories obtained from the food}}\times 100$

Substitute $\text{18 Cal}$ for calories obtained from fats and $\text{154 Cal}$ for calories obtained from food in the above formula as follows:

$\begin{array}{c}\%\text{ of fats}=\frac{\text{18 Cal}}{\text{154 Cal}}\times 100\\ =12\%\end{array}$

Hence, the percentage of calories obtained from fats is $12\%$.

c) In spaghetti,

The number of calories in each product can be calculated as follows:

$\begin{array}{l}\underset{\_}{\begin{array}{c}\text{Fat }1\text{ g}\times \text{9 Cal}/\text{g}=\text{ 9 Cal}\\ \text{Protein }7\text{ g}\times 4\text{ Cal}/\text{g}=\text{ 28 Cal}\\ \text{Carbohydrate }42\text{ g}\times 4\text{ Cal}/\text{g}=168\text{ Cal }\end{array}}\\ \text{Total 205 cal}\end{array}$

Thus, the total number of calories is $\text{205 cal}$.

The percentage of fatscan be calculated as follows:

$\%\text{ of fats}=\frac{\text{Calories obtained from fats}}{\text{Calories obtained from the food}}\times 100$

Substitute $\text{9 Cal}$ for calories obtained from fats and $\text{205 Cal}$ for calories obtained from food in the above formula as follows:

$\begin{array}{c}\%\text{ of fats}=\frac{\text{9 Cal}}{\text{205 Cal}}\times 100\\ =0.0439\times 100\\ =4.4\%\end{array}$

Hence, the percentage of calories obtained from fats is $4.4\%$