Final answer:
Riley needs to work between 9 and 11 whole hours tutoring, alongside her 3 hours of landscaping, to make at least the required $180 while not exceeding a total of 14 work hours for the week.
Step-by-step explanation:
If Riley worked 3 hours landscaping at $9 per hour, she would earn $27 from landscaping.
To find out the possible number of whole hours tutoring she must work, we need to calculate how many hours she needs to work at the tutoring job that pays $18 per hour to make up the difference to meet her minimum requirement of $180.
Since she can only work a maximum of 14 hours a week and has already worked 3 hours landscaping, Riley has 14 - 3 = 11 hours left for tutoring.
The total amount she needs to earn from tutoring is $180 - $27 = $153. Since she makes $18 per hour tutoring, we divide the total amount needed from tutoring by the hourly rate. So, $153 ÷ $18 ≈ 8.5 hours.
Since Riley can't work half hours in this scenario, we'll round up to the nearest whole hour giving us 9 hours. Therefore, Riley must work at least 9 hours tutoring to meet her requirements.
She can work a maximum of 11 hours tutoring since she already worked 3 hours landscaping.
This would give her 3 hours landscaping × $9/hr = $27 from landscaping plus 11 hours tutoring × $18/hr = $198 from tutoring. This totals to $225 for the week, which is still within her requirement of working no more than 14 hours and earning at least $180.
In conclusion, Riley must work between 9 and 11 whole hours tutoring, in addition to her 3 hours landscaping, to earn at least $180 in that week.