A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if x is the number of cheese squares that she eats and y is the number of turkey slices that she eats?

1 answer

To represent the situation with an inequality, we can quantify the total protein intake based on the number of cheese squares and turkey slices that Nina eats.

Let:

  • \( x \) = number of cheese squares
  • \( y \) = number of turkey slices

Each cheese square contains 2 grams of protein, contributing a total of \( 2x \) grams of protein from the cheese squares. Each turkey slice contains 3 grams of protein, contributing a total of \( 3y \) grams of protein from the turkey slices.

Nina wants to consume at least 12 grams of protein. Therefore, the total protein from both cheese squares and turkey slices must be greater than or equal to 12 grams. This can be represented by the following inequality:

\[ 2x + 3y \geq 12 \]

Thus, the inequality that represents the possible ways Nina can eat 12 or more grams of protein is:

\[ 2x + 3y \geq 12 \]