Chapter 22, Problem 22.9E

Interpretation Introduction

Interpretation:

The number of calories from Daily Values (DV) for fat, saturated fat, and total carbohydrate based on a $2000$-calorie diet is to be calculated.

Concept introduction:

The value of percent DV represents the percent of an individual nutrient in one serving of food. For a healthy adult, the value of DV is based on a $2000$-calorie diet. For the proper functioning of body metabolism, it is necessary to take all the mandatory nutrients.

Answer to Problem 22.9E

The number of calories from fat based on a $2000$-calorie diet is $\text{450}\text{cal}$.

The number of calories from saturated fat based on a $2000$-calorie diet is $\text{0}\text{cal}$.

The number of calories from total carbohydrate based on a $2000$-calorie diet is $\text{1150}\text{cal}$.

Explanation of Solution

Total fat per serving is $1\text{g}$.

DV fulfills by $1\text{g}$ fat is $2\%$.

The following formula calculates the DV for fat.

$\text{DV}\text{for}\text{fat}=\frac{\text{Fat}\text{per}\text{serving}\left(\text{g}\right)}{\%\text{Quantity}/100}$…(1)

Substitute the value of fat per serving and percent quantity fulfilled by fat in equation (1).

$\begin{array}{rll}\text{DV}\text{for}\text{fat}& =& \frac{1\text{g}}{2/100}\\ & =& \frac{100}{2}\text{g}\\ & =& \text{50}\text{g}\end{array}$

Therefore, the Daily Values (DV) for fat based on a $2000$-calorie diet is $50\text{g}$.

It is known that $\text{1}\text{g}$ of fat is equivalent to $\text{9}\text{cal}$.

The number of calories in a $\text{2000-calorie}$ diet that should be from fat is calculated as shown below.

$\begin{array}{rll}\text{Number}\text{of}\text{Calories}& =& \text{cal}\text{per}\text{g}\times \text{DV}\\ & =& \text{9×50}\\ & =& \text{450}\text{cal}\end{array}$

Therefore, the number of calories in a $\text{2000-calorie}$ diet that should be from fat is $\text{450}\text{cal}$.

Total saturated fat per serving is $0\text{g}$.

DV fulfills by $0\text{g}$ saturated fat is $0\%$.

The following formula calculates the DV for saturated fat.

$\text{DV}\text{for}\text{saturated}\text{fat}=\frac{\text{Saturated}\text{fat}\text{per}\text{serving}\left(\text{g}\right)}{\%\text{Quantity}/100}$…(2)

Substitute the value of saturated fat per serving and percent quantity fulfilled by saturated fat in equation (2).

$\begin{array}{rll}\text{DV}\text{for}\text{saturated}\text{fat}& =& \frac{0}{\%\text{Quantity}/100}\\ & =& 0\text{g}\end{array}$

Therefore, Daily Values (DV) for saturated fat based on a $2000$-calorie diet is $\text{0}\text{g}$.

It is given that $\text{0}\text{g}$ of saturated fat is present in the $\text{2000-calorie}$ diet, which is equivalent to $\text{0}\text{cal}$.

The number of calories in a $\text{2000-calorie}$ diet that should be from saturated fat is calculated as shown below.

$\begin{array}{rll}\text{Number}\text{of}\text{Calories}& =& \text{cal}\text{per}\text{g}\times \text{DV}\\ & =& \text{0×0}\\ & =& \text{0}\text{cal}\end{array}$

Therefore, the number of calories in a $\text{2000-calorie}$ diet that should be from saturated fat is $\text{0}\text{cal}$.

Total carbohydrate per serving is $23\text{g}$.

DV fulfills by $23\text{g}$ total carbohydrate is $8\%$.

The following formula calculates the DV for total carbohydrate.

$\text{DV}\text{for}\text{total}\text{carbohydrate}=\frac{\text{Total}\text{carbohydrate}\text{per}\text{serving}\left(\text{g}\right)}{\%\text{Quantity}/100}$…(3)

Substitute the value of total carbohydrate per serving and percent quantity fulfilled by total carbohydrate in equation (3).

$\begin{array}{rll}\text{DV}\text{for}\text{total}\text{carbohydrate}& =& \frac{23}{8/100}\text{g}\\ & =& \text{287}\text{.5}\text{g}\end{array}$

Therefore, Daily Values (DV) for total carbohydrate based on a $2000$-calorie diet is $\text{287}\text{.5}\text{g}$.

It is known that $\text{1}\text{g}$ of carbohydrate is equivalent to $\text{4}\text{cal}$.

The number of calories in a $\text{2000-calorie}$ diet that should be from total carbohydrate is calculated as shown below.

$\begin{array}{rll}\text{Number}\text{of}\text{Calories}& =& \text{cal}\text{per}\text{g}\times \text{DV}\\ & =& \text{4}\times \text{287}\text{.5}\\ & =& \text{1150}\text{cal}\end{array}$

Therefore, the number of calories in a $\text{2000-calorie}$ diet that should be from total carbohydrate is $\text{1150}\text{cal}$.

Conclusion

The number of calories from fat based on a $2000$-calorie diet is $\text{450}\text{cal}$.

The number of calories from saturated fat based on a $2000$-calorie diet is $\text{0}\text{cal}$.

The number of calories from total carbohydrate based on a $2000$-calorie diet is $\text{1150}\text{cal}$.