Question 1067098
Let's assume he eats x meatballs, y mushrooms and z eggs.
Then:
Protein: 14x+3y+13z=113   (1)
Fat: 7x+5y+15z=103   (2)
Carbs: 15x+9y+6z=132   (3)
(3)-(2)-(1): we get y:

{{{15x-7x-14x+9y-5y-3y+6z-15z-13z=-84}}}
{{{y=6x+22z-84 (4)}}}

Then we substitute (4) in (1) and (2) and get:
x=4
y=6
z=3