Question

a nutritionist planning a diet for a basketball player wants him to consume 3,650 calories and 650 grams of food daily. calories from carbohydrates and fat will be 60% of the total calories. there are 4, 4, and 9 calories per gram for protein, carbohydrates, and fat, respectively. how many daily grams of fat will the diet include?

Answer 1

210 grams of fat

Step-by-step explanation:

Given that a 3650 calorie diet is 650 grams of food, with 60% of the total calories from carbohydrates and fat, you want to know the number of grams of fat the diet will include if protein, carbohydrates, and fat give 4, 4, and 9 calories per gram, respectively.

Setup

We can write three equations based on the given information. Let p, c, f represent grams of protein, carbohydrates, and fat, respectively. Then we have ...

p +c +f = 650 . . . . . . . . total grams

4p +4c +9f = 3650 . . . . total calories

0p +4c +9f = 0.60·3650 . . . . calories from carbs and fat

Solution

The attachment shows a calculator solution to this system of equations. It tells us the diet should include ...

210 grams of fat

Ad Hoc solution

Subtracting the 3rd equation from the 2nd, we have ...

(4p +4c +9f) -(4c +9f) = 3650 -0.6·3650

4p = 0.4·3650

p = 365

Solving the first equation for c gives ...

365 +c +f = 650

c = 285 -f

Substituting into the last equation, we have ...

4(285 -f) +9f = 2190

5f = 1050 . . . . . . . . . . . . subtract 1140

f = 210 . . . . . . . . . . . . divide by 5

The diet will include 210 daily grams of fat.

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