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 the inequality for the number of weeks 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 per week
3. Total amount needed to buy the cellphone: $300

After \( x \) weeks, the total amount of money Lily will have is given by the initial amount plus her earnings over those weeks:

\[ 40 + 65x \]

We want this amount to be at least $300, leading to the inequality:

\[ 40 + 65x \geq 300 \]

To find the number of weeks \( x \), we can solve the inequality:

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 inequality is:

\[ 65x + 40 \geq 300 \]

Lily must save for at least 4 weeks to have at least $300.