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Mike plans a diet for his dog Scout that includes a combination of dog food and treats each day.

Scout eats between 510 and 540 calories per day. The inequality 510 ≤ 480 + 15x ≤ 540, can be used to
represent the situation, where x is the number of treats Scout can have each day.

2 Answers

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Final answer:

To convert a person’s caloric intake to Watts, we use the equivalence of 1 kcal to 4.184 kJ. A smaller or less active person needing 1,300 kcal/day represents an energy intake rate measured in Watts, while 2,000 kcal/day approximates to about 100 Watts, considering the energy expenditure of athletic activities.

Step-by-step explanation:

Understanding Caloric Intake and Energy Expenditure

To convert the daily intake of kilocalories (kcal) to Watts (W), we can use the understanding that 1 kcal is equivalent to 4.184 kilojoules (kJ). For example, a smaller or less active person consuming 1,300 kcal per day would have an energy intake rate which can be approximated in Watts. Similarly, a 2,000 kcal daily intake translates to roughly 100 Watts when converted to energy per time unit. Given that most athletic activities consume energy at a rate of 400 to 500 Watts, a single cup of yogurt containing 325 kcal could replace the energy expended by high-intensity exercises in a relatively short amount of time.

By understanding the energy content of food (measured in kcal) and the power of physical activities (measured in Watts), individuals can better manage their diet and exercise routines. However, due to individual variation in metabolism and the inefficiencies involved in converting food energy to physical work, approximate values are often used for practical purposes.

User Dmitriano
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Final answer:

To find the number of treats Scout can have, subtract 480 from all parts of the inequality 510 ≤ 480 + 15x ≤ 540 then divide by 15 to get 2 ≤ x ≤ 4. Hence, Scout can have between 2 and 4 treats per day according to the given caloric limits.

Step-by-step explanation:

The student's question concerns how to determine the number of treats Scout the dog can have each day based on his caloric needs and an inequality that represents the combination of calories from dog food and treats.

To solve the inequality 510 ≤ 480 + 15x ≤ 540, where x represents the number of treats, we first subtract 480 from all parts of the inequality, yielding 30 ≤ 15x ≤ 60.

Next, we divide by 15 to solve for x, which gives us the inequality 2 ≤ x ≤ 4.

Therefore, Scout can have between 2 and 4 treats each day. This exercise is an application of solving linear inequalities, which is a fundamental concept in high school mathematics.

User Opedge
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