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Chapter 2: Problem 6

Tab and Crystal both own cats. a. Tab buys a 3-pound bag of cat food every 30 days. At what rate does his cat eat the food? (a) b. Crystal buys a 5 -pound bag of cat food every 45 days. At what rate does her cat eat the food? c. Whose cat, Tab's or Crystal's, eats more food per day? (h)

Short Answer

Expert verified
Crystal's cat eats more food per day at approximately 0.111 pounds.

Step by step solution

01

Determine Tab's Cat's Eating Rate

To find how much Tab's cat eats per day, we need to divide the total amount of food by the number of days. Tab buys a 3-pound bag, and it lasts for 30 days. Therefore, the daily rate for Tab's cat is: \[ \frac{3 \, \text{pounds}}{30 \, \text{days}} = 0.1 \, \text{pounds per day}. \]
02

Determine Crystal's Cat's Eating Rate

Next, we calculate how much Crystal's cat eats per day. Crystal buys a 5-pound bag, and it lasts for 45 days. The daily consumption rate for Crystal's cat is calculated as follows: \[ \frac{5 \, \text{pounds}}{45 \, \text{days}} = \frac{1}{9} \, \text{pounds per day} \approx 0.111 \, \text{pounds per day}. \]
03

Compare the Eating Rates

To determine which cat eats more food daily, we compare the two rates. Tab's cat eats 0.1 pounds per day, while Crystal's cat eats approximately 0.111 pounds per day. Since 0.111 is greater than 0.1, Crystal's cat eats more food per day.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit Rates
Unit rates are essential for understanding how a quantity changes relative to another. In this exercise, we are looking at the rate at which cats consume food. Specifically, a unit rate tells us how much of a resource is used per single unit of time, such as days. For Tab's cat, we calculated the unit rate by dividing 3 pounds of food by 30 days. This gave us a rate of 0.1 pounds per day. Similarly, for Crystal's cat, dividing 5 pounds by 45 days resulted in a rate of approximately 0.111 pounds per day.
Understanding unit rates is crucial as they provide a clear picture of consistent consumption or use patterns and make comparisons simpler. In practical terms, unit rates are widely used to determine the efficiency or needs in various everyday activities.
Comparative Analysis
Comparative analysis involves evaluating two or more sets of data to identify patterns or differences. In the given exercise, we performed a comparative analysis by examining the daily food consumption rates of Tab's and Crystal's cats. This analysis helps to visualize which cat has a higher intake based on the unit rates calculated.
This type of analysis is not limited to this context; it is useful in numerous fields, including economics, business, and personal finance, where decision-making often requires a clear understanding of differences and similarities in performance metrics. In our specific scenario, the comparison revealed that Crystal's cat consumes more food per day compared to Tab's cat.
Ratio and Proportion
Ratios and proportions are mathematical concepts used to describe relationships between quantities. In the exercise with Tab and Crystal's cats, the initial problem provides different bags of cat food and the duration they last. By setting up ratios of pounds of food to days, we establish a direct relationship that helps determine each cat's consumption pattern.
For instance, Tab's ratio of 3 pounds to 30 days simplifies to a consumption of 0.1 pounds per day, whereas Crystal鈥檚 5 pounds to 45 days simplifies to approximately 0.111 pounds per day. Ratios provide insights into consistent patterns of usage, while proportions can help predict future needs by maintaining these ratios. Understanding these concepts aids in anticipating needs and making informed decisions based on predictable consumption behaviors.

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Most popular questions from this chapter

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