Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if [tex]$x$[/tex] is the number of cheese squares that she eats and [tex]$y$[/tex] is the number of turkey slices that she eats?
[tex]$12 \leq x+y$[/tex]
[tex]$12 \geq x+y$[/tex]
[tex]$12 \leq 2 x+3 y$[/tex]
[tex]$12 \geq 2 x+3 y$[/tex]
Answer (2)
The inequality that represents the ways Nina can consume 12 or more grams of protein from cheese squares and turkey slices is 2 x + 3 y ≥ 12 . This accounts for the protein contribution from both food items. Therefore, the correct option is 12 ≤ 2 x + 3 y .
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Calculate the total protein from cheese squares: 2 x .
Calculate the total protein from turkey slices: 3 y .
The total protein intake is the sum of protein from cheese squares and turkey slices: 2 x + 3 y .
Nina wants to eat 12 or more grams of protein, so the inequality is 2 x + 3 y ≥ 12 .
12 ≥ 2 x + 3 v
Explanation
Problem Analysis Let's analyze the problem. We are given that each cheese square has 2 grams of protein and each turkey slice has 3 grams of protein. Nina wants to eat at least 12 grams of protein. We need to find the inequality that represents this situation, where x is the number of cheese squares and y is the number of turkey slices.
Formulating the Inequality The total protein from cheese squares is 2 x grams, and the total protein from turkey slices is 3 y grams. The total protein intake is the sum of these two, which is 2 x + 3 y . Since Nina wants to eat 12 or more grams of protein, we have the inequality 2 x + 3 y ≥ 12 .
Final Inequality Therefore, the inequality that represents the possible ways Nina can eat 12 or more grams of protein is 2 x + 3 y ≥ 12 .
Examples
This type of problem is useful in diet planning. For example, if you need to consume a certain amount of nutrients daily, and you have different food options with varying amounts of those nutrients, you can use inequalities to determine the possible combinations of foods that meet your nutritional goals. This helps in making informed decisions about your diet to ensure you are getting enough of the nutrients you need.
