To write an inequality for the number of weeks \( x \) Lily will need to save to have at least $300, we can start by considering her initial savings and her weekly earnings.
- Initial savings from her grandfather: $40
- Weekly earnings from tutoring: $65 per week
- Total amount needed: $300
Lily's total savings after \( x \) weeks can be expressed as:
\[ \text{Total savings} = 40 + 65x \]
To find out when this amount will be at least $300, we set up the inequality:
\[ 40 + 65x \geq 300 \]
Next, we can solve 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 we established is:
\[ x \geq 4 \]
Conclusion
Lily must save for at least 4 weeks to have at least $300. The solution \( x \geq 4 \) means that Lily can save for 4 weeks or more in order to reach her goal of $300.