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?

12 ≤ x + y
12 ≥ x + y
12 ≤ 2x + 3y
12 ≥ 2x + 3y

1 answer

To express the requirement that Nina can eat 12 or more grams of protein using cheese squares (which have 2 grams of protein each) and turkey slices (which have 3 grams of protein each), we can set up the inequality based on the total protein content contributed by each food type:

  • Each cheese square contributes 2 grams of protein, so \(2x\) represents the protein from \(x\) cheese squares.
  • Each turkey slice contributes 3 grams of protein, so \(3y\) represents the protein from \(y\) turkey slices.

To find the total protein consumed, we combine these contributions:

\[ \text{Total protein} = 2x + 3y \]

To meet her requirement of consuming at least 12 grams of protein, we set up the inequality:

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

This can be rearranged to fit common notation, but the form \(2x + 3y \geq 12\) correctly represents the situation.

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

12 ≤ 2x + 3y.