Answer:
240 grams of fat.
Step-by-step explanation:
let
c = grams of carbohydrates
p =grams of proteins
f = grams of fat.
Then from the information given:
[tex]4c+4p+9f=3800\:calories.[/tex]
And since 60% of the calories should come from carbohydrates and fats (which is 2280 calories)
[tex]4c+9f =2280\:calories[/tex]
And
[tex]c+p+f=650g.[/tex]
Thus we have three equations:
(1).[tex]4c+4p+9f=3800\:calories.[/tex]
(2).[tex]4c+9f =2280\:calories[/tex]
(3).[tex]c+p+f=650g.[/tex]
We put equation (2) into equation (1) and solve for [tex]p[/tex]:
[tex]2280+4p=3800[/tex]
[tex]\therefore \boxed{p =380\:grams}[/tex]
Now we put this value of [tex]p[/tex] into equation (3) and get:
[tex]c+f=270\:grams.[/tex]
Now from this equation we solve for c and get:
[tex]c=270-f.[/tex]
And put this value of [tex]c[/tex] into equation (2) and solve for[tex]f[/tex]:
[tex]4(270-f)+9f=2280.\\\\\therefore \boxed{f= 240 grams}[/tex]
Thus the diet will include 240 grams of fat.
