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

__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.

Answer 1

To write an inequality for the number of weeks \( x \) that Lily will need to save, we can start by considering her initial amount and her weekly earnings.

1. Initial amount from her grandfather: $40
2. Weekly earnings from tutoring: $65
3. Total amount needed to buy the phone: $300

After \( x \) weeks of tutoring, the total amount of money Lily will have is the initial amount plus the money she earns from tutoring.

This can be expressed as: \[ 40 + 65x \]

We want this amount to be at least $300. Therefore, we can set up the inequality: \[ 40 + 65x \geq 300 \]

Now, we can simplify this inequality to find the number of weeks \( x \) that Lily needs to save:

1. Subtract 40 from both sides: \[ 65x \geq 300 - 40 \] \[ 65x \geq 260 \]

2. Divide both sides by 65: \[ x \geq \frac{260}{65} \] \[ x \geq 4 \]

Thus, the final inequality is: \[ x + 4 \geq 0 \] (fill in \( x + 4 \), but expression is differentiated. We need \( x \geq 4 \)).

Summary:

• The correct inequality for the number of weeks is: \[ 65x + 40 \geq 300 \]
• The solution to this inequality is: Lily must save for at least 4 weeks to have at least $300.