Chapter 18, Problem 61E

Interpretation Introduction

Interpretation:

The percentage of total 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 61E

Solution:

a) $43\%$.

b) $45\%$.

c) $9.3\text{ \%}$.

Explanation of Solution

a) In Little Debbie choco-cakes,

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

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

$\begin{array}{l}\underset{\_}{\begin{array}{l}\text{Fat }13\text{ g}\times \text{9 Cal}/\text{g}=\text{ 117 Cal}\\ \text{Protein 2 g}\times 4\text{ Cal}/\text{g }=\text{ 8 Cal}\\ \text{Carbohydrate }37\text{ g}\times 4\text{ Cal}/\text{g }=148\text{ Cal }\end{array}}\\ \text{Total 273 cal}\end{array}$

Thus, the total number of calories obtained is $\text{273 cal}$.

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 $\text{117 Cal}$ for calories obtained from fats and $\text{273 Cal}$ for calories obtained from food in the above formula as follows:

$\begin{array}{c}\%\text{ of fats}=\frac{\text{117 Cal}}{\text{273 Cal}}\times 100\\ =0.429\times 100\\ =43\%\end{array}$

Therefore, the percentage of calories obtained from fats is $43\%$.

b) In aSnickers bar,

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

$\begin{array}{l}\underset{\_}{\begin{array}{l}\text{Fat }14\text{ g}\times \text{9 Cal}/\text{g}=\text{ 126 Cal}\\ \text{Protein }4\text{ g}\times 4\text{ Cal}/\text{g}=\text{ 16 Cal}\\ \text{Carbohydrate }35\text{ g}\times 4\text{ Cal}/\text{g}=\text{ 140 Cal }\end{array}}\\ \text{Total 282 cal}\end{array}$

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 $\text{126 Cal}$ for calories obtained from fats and $\text{282 Cal}$ for calories obtained from food in the above formula as follows:

$\begin{array}{c}\%\text{ of fats}=\frac{\text{126 Cal}}{\text{282 Cal}}\times 100\\ =0.447\times 100\\ =45\%\end{array}$

Therefore, the percentage of calories obtained from fats is $45\%$.

c) In Jerseymaid peach yoghurt,

The number of calories in each product can be calculated asfp;; pws:

$\begin{array}{l}\underset{\_}{\begin{array}{c}\text{Fat }2.5\text{ g}\times \text{9 Cal}/\text{g}=\text{ 22}\text{.5 Cal}\\ \text{Protein }9.0\text{ g}\times 4\text{ Cal}/\text{g}=36.0\text{ Cal}\\ \text{Carbohydrate }47.0\text{ g}\times 4\text{ Cal}/\text{g}=188.0\text{ Cal }\end{array}}\\ \text{Total 247 cal}\end{array}$

Thus, the total number of calories obtained is $247\text{ cal}$.

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 $\text{23 Cal}$ for calories obtained from fats and $\text{247 Cal}$ for calories obtained from food in the above formula as follows:

$\begin{array}{c}\%\text{ of fats}=\frac{\text{23 Cal}}{\text{247 Cal}}\times 100\\ =0.093\times 100\\ =9.3\%\end{array}$

Therefore, the percentage of calories obtained from fats is $9.3\%$