Final answer:
Leah can work between 7 and 9 whole hours tutoring, coupled with her 5 hours of clearing tables, to meet her weekly goal of working a maximum of 14 hours and earning at least $200.
Step-by-step explanation:
The question asks us to determine all possible values for the number of whole hours Leah must tutor if she worked 5 hours clearing tables to meet her minimum earning requirement of $200 per week. She earns $22 per hour tutoring and $10 per hour clearing tables, and she can work at most 14 total hours per week.
First, we calculate the earnings from clearing tables for 5 hours: 5 hours × $10/hour = $50.
Now, we need to find how many hours Leah needs to work tutoring to make up the remaining amount to reach at least $200.
Since she has already worked 5 hours clearing tables, she can work up to 14 - 5 = 9 hours tutoring.
The total earnings from tutoring must be at least $200 - $50 = $150.
To find out the minimum hours Leah needs to tutor, we can set up an inequality: $22 × hours tutoring ≥ $150. Dividing both sides by $22 gives us the number of hours tutoring ≥ $150 / $22 ≈ 6.82.
Since she can only work whole hours and she needs at least $150, Leah must work at least 7 hours of tutoring.
To satisfy both conditions of working at most 14 hours a week and earning a minimum of $200, Leah must work between 7 and 9 whole hours tutoring, provided she has already worked 5 hours clearing tables.