Applied Math - Percentages - Nutrition

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Introduction

Percentages are often used as guidelines for a healthy diet.

Example:

1.

An adult is said to need 0.8 grams of protein per kilogram of body weight. One particular adult is 82 kilograms.

A serving of black beans is 6 grams of protein. What percent of daily protein needs are met by this serving of black beans?

To calculate a percentage, we divide an amount we are interested in (the serving of protein in black beans, 6 grams) by a starting amount or a total (the total grams of protein needed for the individual). We need to calculate the total grams of protein this individual needs.

If a person needs 0.8 gram of protein per kilogram of body weight, and if the person is 82 kilograms, then the person needs

\[\frac{0.8 \text{ g}}{1 \text{ kilogram}} \cdot 82 \text{ kilograms} = \frac{0.8 \text{ g}}{1 \cancel{\text{ kilogram}}} \cdot 82 \cancel{\text{ kilograms}} = 0.8 \cdot 82 \text{ g} = 65.6 \text{ g}\]

The percentage of daily protein for 6 grams of protein is

\[\frac{6 \text{ g}}{65.6 \text{ g}} \cdot 100\% = 9.15 \%\]



2.

A particular granola bar is 18.9 grams of carbohydrates, 4 grams of fat, and 2 grams of protein. What percentage of the granola bar is carbohydrates by weight?

To calculate a percentage, divide the amount you are interested in (carbohydrates) by the starting amount or total (total grams of the bar) then multiply by 100.

\[\frac{18.9}{24.9} \cdot 100 = 75.9\%\] of the granola bar is carbohydrates



3.

A dietitian has asked that a person get 35% of their calories from protein. If they are allowed 2,000 calories per day in their diet, how many calories must come from protein?

To calculate a percentage of a number, multiply by the decimal form of the percentage.

\[2,000 \text{ calories} \cdot 0.35 = 700\] calories from protein.

Practice Problems

1. An adult is said to need 0.8 grams of protein per kilogram of body weight. One particular adult is 68 kilograms.

A serving of tofu is 10 grams of protein. What percent of daily protein needs are met by this serving of tofu?



2. A serving of a particular brand of pasta is 38 grams of carbohydrates, 7.7 grams of protein and 0.6 grams of fats. What percentage of the pasta is protein by weight?



3. A dietitian has asked that a person get no more than 45% of their calories from carbohydrates. If they are allowed 2,000 calories per day in their diet, what is the maximum amount of calories allowed from carbohydrates?

Theory Questions

1. If a person limits themselves to 2,000 calories per day but wants more protein in their diet, what sort of foods should they be looking to consume? What percentages are they looking for in those foods?