Question

A nutritionist planning a diet for a runner wants him to consume 3,800 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

Answer: It's actually 210 g

(Excuse my answer, I made a math error)

Answer 2

240 grams of fat.

Explanation:

let

c = grams of carbohydrates

p =grams of proteins

f = grams of fat.

Then from the information given:

`4c+4p+9f=3800\:calories.`

And since 60% of the calories should come from carbohydrates and fats (which is 2280 calories)

`4c+9f =2280\:calories`

And

`c+p+f=650g.`

Thus we have three equations:

(1).
`4c+4p+9f=3800\:calories.`

(2).
`4c+9f =2280\:calories`

(3).
`c+p+f=650g.`

We put equation (2) into equation (1) and solve for
`p`:

`2280+4p=3800`

`\therefore \boxed{p =380\:grams}`

Now we put this value of
`p` into equation (3) and get:

`c+f=270\:grams.`

Now from this equation we solve for c and get:

`c=270-f.`

And put this value of
`c` into equation (2) and solve for
`f`:

`4(270-f)+9f=2280.\\\\\therefore \boxed{f= 240 grams}`

Thus the diet will include 240 grams of fat.