Question

An average person can maintain their weight on a 2.0x10^3 kcal/day diet. Some doctors recommend balancing the intake with a ratioof 35. % protein, 45.% carbohydrate and 20.% lipids. How many grams of each type of nutrient do these percentages represent?

Answer 1

1) List the known and unknown quantities.

Calories per day: 2.0*10^3 kcal/day diet.

Type of nutrients and percentages:

Protein: 35.%

Carbohydrate: 45.%

Lipids: 20.%

2) 4-9-4 rule.

When talking about food calories, this rule states that 1 g of protein equals 4 kcal, 1 g of carbohydrate equals 4 kcal, and 1 g of lipids equals 9 kcal.

3) Grams of protein.

3.1-kcal from protein.

`kcal\text{ }protein=2.0*10^3*(35)/(100)=700\text{ }kcal`

3.2-Convert kcal of protein to grams of protein

`g\text{ }protein=700\text{ }kcal\text{ }protein*\frac{1\text{ }g\text{ }protein}{4\text{ }kcal}=175\text{ }g\text{ }protein`

4) Grams of carbohydrates.

4.1-kcal from carbohydrates.

`kcal\text{ }carbohydrates=2.0*10^3\text{ }kcal*(45)/(100)=900\text{ }kcal\text{ }carbohydrates`

4.2-Convert kcal of carbohydrates to grams of carbohydrates.

`g\text{ }carbohydrates=900\text{ }kcal\text{ }carbohydrates*\frac{1\text{ }g\text{ }carbohydrates}{4\text{ }kcal}=225\text{ }g\text{ }carbohydrates`

5) Grams of lipids.

5.1-kcal from lipids.

`kcal\text{ }lipids=2.0*10^3\text{ }kcal*(20)/(100)=400\text{ }kcal\text{ }lipids`

5.2-Convert kcal of lipids to grams of lipids.

`g\text{ }lipids=400\text{ }kcal\text{ }lipids*\frac{1\text{ }g\text{ }lipid}{9\text{ }kcal}=44.44\text{ }g\text{ }lipids`

How many grams of each type of nutrient?

Protein: 175 g

Carbohydrates: 225 g

Lipids: 44.4 g

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