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.(4 points)
Let's let the variable x represent the number of weeks Lily needs to save.
Since Lily saves $65 each week after school, she will save a total of 65x dollars after x weeks.
In addition, her grandfather gives her $40, so the total amount of money Lily will have saved after x weeks is 65x + 40 dollars.
We want this total amount of saved money to be at least $300, so the inequality is:
65x + 40 ≥ 300.
To find the number of weeks Lily will need to save to have at least $300, we need to solve this inequality.
The solutions to this inequality are all values of x that make the left side of the inequality greater than or equal to the right side.
Solving the inequality:
65x + 40 ≥ 300
Subtracting 40 from both sides:
65x ≥ 260
Dividing both sides by 65:
x ≥ 4
The solutions to the inequality are x ≥ 4. This means that Lily will need to save for at least 4 weeks in order to have at least $300.