Ivy earns \( \$ 25 \) an hour tutoring students and \( \$ 12 \) an hour working at the library. She wants to earn at least \( \$ 150 \) in a week, but is not able to work for more than 8 hours. (i) Write down an inequality to represent the above information. Define the variables used. ii) State all the possible combinations of hours that Ivy could tutor or work at the library.

Let \( x \) be the number of hours Ivy tutors students, and \( y \) be the number of hours she works at the library. The inequalities that represent Ivy’s situation are: 1. \( 25x + 12y \geq 150 \) (to ensure she earns at least $150) 2. \( x + y \leq 8 \) (to ensure she doesn’t work more than 8 hours) To find all possible combinations of hours that Ivy could work, we can solve the inequalities. The minimum earnings can be calculated based on different combinations of hours spent tutoring and working at the library while respecting the working hour limit. This would involve setting \( x \) and \( y \) as nonnegative integers (since she can't work negative hours), and checking values for \( x \) and \( y \) accordingly within constraints. Possible combinations include: - Tutoring for 0 hours and working at the library for 8 hours (earning $96), - Tutoring for 6 hours and 2 hours at the library (earning $162), - Tutoring for 4 hours and 4 hours at the library (earning $148), - Tutoring for 5 hours and working for 2 hours at the library (earning $157), and so on, always looking to meet the earning threshold while balancing the total hours up to 8!