Questions: Modeling with Systems of Inequalities 1. Selena is the manager for the high school football team. She is responsible for helping organize a wholesome breakfast for the team. Today, the team is getting whole wheat pancakes and bacon. The coach wants to make sure that the team's breakfast provides them with the appropriate calories (enough to feel full, but not so much that it could compromise their game play) and a limited amount of sodium. Specifically, the coach has requested that the meal provide between 550 to 850 total calories and no more than 1,000 mg of sodium. Selena does some research to find out the calorie and sodium content of each pancake and slice of bacon, she discovers the following information: - Calories Sodium (mg) - Slice of Bacon 54 178 - Pancake 175 125 Selena needs to know all the combinations of pancakes and bacon that a player could eat for breakfast and still keep within the coach's calorie and sodium requirements. (Assume that players eat entire pancakes and unbroken pieces of bacon.) (a) Write a system of inequalities to model this scenario, and graph the system.

Modeling with Systems of Inequalities 1. Selena is the manager for the high school football team. She is responsible for helping organize a wholesome breakfast for the team. Today, the team is getting whole wheat pancakes and bacon. The coach wants to make sure that the team's breakfast provides them with the appropriate calories (enough to feel full, but not so much that it could compromise their game play) and a limited amount of sodium. Specifically, the coach has requested that the meal provide between 550 to 850 total calories and no more than 1,000 mg of sodium. Selena does some research to find out the calorie and sodium content of each pancake and slice of bacon, she discovers the following information: - Calories Sodium (mg) - Slice of Bacon 54 178 - Pancake 175 125 Selena needs to know all the combinations of pancakes and bacon that a player could eat for breakfast and still keep within the coach's calorie and sodium requirements. (Assume that players eat entire pancakes and unbroken pieces of bacon.) (a) Write a system of inequalities to model this scenario, and graph the system.
Transcript text: Modeling with Systems of inequalities 1. Selena is the manager for the high school football team. She is responsible for helping organize a wholesome breakfast for the team. Today, the team is getting whole wheat pancakes and bacon. The coach wants to make sure that the team's breakfast provides them with the appropriate calories (enough to feel full, but not so much that it could compromise their game play) and a limited amount of sodium. Specifically, the coach has requested that the meal provide between 550 to 850 total calories and no more than 1,000 mg of sodium. Selena does some research to find out the calorie and sodium content of each pancake and slice of bacon, she discovers the following information: \begin{tabular}{l|l|c|c|} \hline & Calories & Sodium (mg) \\ \hline Slice of Bacon & 54 & 178 \\ \hline Pancake & 175 & 125 \\ \hline \end{tabular} Selena needs to know all the combinations of pancakes and bacon that a player could eat for breakfast and still keep within the coach's calorie and sodium requirements. (Assume that players eat entire pancakes and unbroken pieces of bacon.) (a) Write a system of inequalities to model this scenario, and graph the system.
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Solution

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Solution Steps

Step 1: Define the variables

Let 'b' represent the number of bacon slices and 'p' represent the number of pancakes.

Step 2: Set up the calorie inequality

The total calories should be between 550 and 850. Each slice of bacon has 54 calories, and each pancake has 175 calories. Thus, the inequality is:

550 ≤ 54b + 175p ≤ 850

Step 3: Set up the sodium inequality

The total sodium should be no more than 1000mg. Each slice of bacon has 178mg of sodium, and each pancake has 125mg. Thus, the inequality is:

178b + 125p ≤ 1000

Final Answer:

The system of inequalities is:

550 ≤ 54b + 175p ≤ 850 178b + 125p ≤ 1000

where 'b' represents slices of bacon and 'p' represents pancakes.

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