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)

Question

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.

GPT-4o mini · Answer

To write an inequality for the number of weeks Lily will need to save, let's define the variables and constants involved.

Let $ x $ represent the number of weeks Lily tutors.
Lily starts with $40 from her grandfather.
She earns $65 each week from tutoring.
She needs at least $300 to buy the cellphone.

The total amount of money Lily will have after $ x $ weeks is represented by the equation: \[ 40 + 65x \]

We want this amount to be at least $300: \[ 40 + 65x \geq 300 \]

To solve for $ x $, we first isolate the term with $ x $: \[ 65x \geq 300 - 40 \] \[ 65x \geq 260 \]

Next, we divide both sides by 65: \[ x \geq \frac{260}{65} \] \[ x \geq 4 \]

Thus, we have our inequality: \[ x \geq 4 \]

Solution Description:

Lily must save for at least 4 weeks to have at least $300. Any number of weeks $ x $ that is 4 or greater will satisfy the requirement for her to purchase the cellphone. This means that if she tutors for 4 weeks, she will have exactly $300, and if she tutors for more than 4 weeks, she will have more than $300.