.
Let x be the number of the marinated mushroom caps;
y be the number of the spicy meatball;
z be the number of the deviled eggs.
According to the condition, these tree balance equations are in place:
3x + 14y + 13z = 114 grams of protein (1)
5x + 7y + 15z = 95 grams of fat (2)
9x + 15y + 6z = 141 grams of carbohydrate (3)
So, what Ron must do is to input the coefficients of the matrix and the right side terms into his calculator and then press the button .
Then he will obtain the answer.
Instead of calculator, I used this popular free of charge online solver in this site
https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver
written by our colleague Jim Thompson to get this answer:
x = 6 (marinated mushroom caps),
y = 5 (spicy meatball),
z = 2 (deviled eggs).
Solved.