Final Answer
Sasha's daily calorie burn, considering X as the minutes spent kickboxing and Y as the minutes spent running, can be modeled by the inequality: \(30X + 21Y \geq 5500\).
Step-by-step explanation:
To determine the inequality representing Sasha's daily calorie burn, we consider the calories burned per minute during kickboxing (30 calories) and running (21 calories). The total calories burned per day should be at least 5500. Therefore, the inequality is formed as \(30X + 21Y \geq 5500\), where X represents the minutes spent kickboxing and Y represents the minutes spent running.
Kickboxing burns 30 calories per minute, so the total calories burned during kickboxing can be represented as 30X. Running burns 21 calories per minute, so the total calories burned during running can be represented as 21Y. Adding these together gives the total daily calorie burn: 30X + 21Y. To satisfy Sasha's goal of burning at least 5500 calories per day, the sum of these burns must be greater than or equal to 5500, hence the inequality \(30X + 21Y \geq 5500\).
This inequality ensures that Sasha meets her daily calorie burn goal by accounting for the combined effects of kickboxing and running. It provides a guideline for the minimum amount of time she needs to spend on each activity to achieve or surpass the targeted calorie expenditure. Adjusting the values of X and Y within this inequality will allow Sasha to plan her exercise routine while ensuring she meets her calorie-burning objective for the day.