Lily is saving up to buy a cellphone. She needs to save at least $300 before she is able to buy the phone. Her grandfather gives her $40, and she earns $65 tutoring after school each week.
Write an inequality for the number of weeks Lily will need to save to have at least $300, and describe the solutions.
Let's say the number of weeks Lily needs to save is represented by w.
The amount of money Lily earns after tutoring in w weeks is given by 65w.
Taking into account the $40 her grandfather gives her, the total amount of money Lily will have after w weeks is given by 65w + 40.
The inequality for the number of weeks Lily needs to save to have at least $300 is:
65w + 40 >= 300.
To describe the solutions, we solve the inequality:
65w >= 260,
w >= 260/65,
w >= 4.
Therefore, Lily will need to save for at least 4 weeks to have at least $300. This means that if she saves for exactly 4 weeks, she will have $260, but if she saves for 5 weeks, she will have $325, which is more than the $300 she needs.