Question

Based on the graph and the inequality x + y ≥ 300, the possible solution is 40 hours tutoring and 20 hours walking dogs.

Answer 1

The proposed solution of 40 hours of tutoring and 20 hours of walking dogs does not satisfy the inequality x + y ≥ 300, as the total hours amount to only 60. In scenarios involving work and income, variables typically represent different economic choices, such as labor hours and earned income.

Step-by-step explanation:

Based on the inequality x + y ≥ 300, and considering the context of the question, where x represents the number of hours spent tutoring and y represents the number of hours spent walking dogs, we can evaluate the given solution of 40 hours tutoring and 20 hours walking dogs. Plugging in the values, we get 40 + 20 which equals 60. Since 60 is greater than the required minimum of 300, the statement is false, and this solution does not satisfy the inequality provided.

In terms of economic choices and labor-leisure trade-offs, as related to the budget constraint models described in the various figures and examples (e.g., budget lines and government assistance impacts), the situation would typically involve assessing how different combinations of work hours and leisure or other non-paid activities affect one's overall income and utility.

Example 12.4, for instance, illustrates how Svetlana's income from each tutoring session can be calculated using the linear equation, y = 25 + 15x. This equation can help to understand how changes in the number of tutoring hours (the independent variable x) influence her total income (the dependent variable y).

Answer 2

The question is about solving an inequality to check if 40 hours of tutoring and 20 hours of walking dogs meet the required total of 300 hours or more. The solution 40 + 20 equals 60, which does not satisfy the inequality x + y ≥ 300.

Step-by-step explanation:

The question pertains to solving an inequality representing a combination of hours spent tutoring and walking dogs that meet a certain requirement. In this case, we're given the inequality x + y ≥ 300, where 'x' represents the number of hours spent tutoring and 'y' represents the hours spent walking dogs. To determine if the proposed solution of 40 hours of tutoring and 20 hours of walking dogs is valid, we substitute these values into the inequality to get 40 + 20 ≥ 300.

If the inequality holds true, then the combination of hours is a possible solution. Otherwise, the student will need to find a different combination. It's clear that 40 + 20 equals 60, which does not satisfy the inequality x + y ≥ 300; hence, 40 hours of tutoring and 20 hours of walking dogs is not a valid solution.