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... give the full inequality
Let's denote the number of weeks Lily needs to save as "w".
The amount of money Lily earns each week from tutoring can be represented as 65w.
The inequality for the number of weeks Lily will need to save to have at least $300 is:
65w + 40 ≥ 300
This inequality states that the total amount of money Lily earns from tutoring ($65 multiplied by the number of weeks, w) plus the amount her grandfather gives her ($40) must be greater than or equal to $300.
The solutions to this inequality include any positive whole number value of w that satisfies the inequality. As Lily earns $65 per week and receives $40 from her grandfather, the inequality will be satisfied once Lily has saved up enough money over a number of weeks to reach or exceed $300.
answer the question
Apologies for the confusion. The full inequality for the number of weeks Lily will need to save to have at least $300 is:
65w + 40 ≥ 300
The solutions to this inequality are any positive whole number values of w that satisfy the inequality. In other words, the number of weeks Lily needs to save must be equal to or greater than the smallest whole number that satisfies the inequality.
Let's first define a variable to represent the number of weeks Lily needs to save. Let's call it "w".
Now, let's break down the information given in the problem:
- Lily's grandfather gives her $40.
- Lily earns $65 tutoring after school each week.
To determine how much money Lily will have after "w" weeks, we can use the following equation:
Total Money = Grandfather's Money + Tutoring Money
Grandfather's Money = $40
Tutoring Money = $65 * w (since Lily earns $65 every week she tutors)
Total Money = $40 + $65w
According to the problem, Lily needs to save at least $300. Hence, we can write the inequality:
$40 + $65w ≥ $300
This is the full inequality that represents the number of weeks Lily will need to save in order to have at least $300.