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.(2 points) x+ ≥ , where x is the number of weeks Lily will need to save. Lily must save for at least weeks to have at least $300.

Question

GPT-4o mini · Answer

To create an inequality for the number of weeks Lily will need to save, we start by noting her initial amount and her earnings per week.

Lily starts with $40 from her grandfather.
She saves $65 each week from tutoring.

We want to find the minimum number of weeks, represented by $ x $, that she needs to save to have at least $300.

The total amount Lily will have after $ x $ weeks is: \[ 40 + 65x \]

We need this total to be at least $300, so we can write the inequality as: \[ 40 + 65x \geq 300 \]

Next, we will solve the inequality for $ x $:

Subtract 40 from both sides: \[ 65x \geq 300 - 40 \] \[ 65x \geq 260 \]
Divide both sides by 65: \[ x \geq \frac{260}{65} \] \[ x \geq 4 \]

Thus, the inequality is: \[ x \geq 4 \]

Description of the solutions: The solution to this inequality means that Lily must save for at least 4 weeks in order to have enough money, which includes the initial $40 given by her grandfather and her earnings from tutoring. If $ x = 4 $, she will have exactly $300, while any value greater than 4 represents a situation where she has more than $300 saved.