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

Let's break down the problem step by step.

Lily starts with $40 from her grandfather. Each week, she earns $65 from tutoring. We need to find the inequality that represents how much money Lily has after saving for \( x \) weeks.

The total amount of money she will have after \( x \) weeks can be expressed as:

\[ 40 + 65x \]

Lily wants this amount to be at least $300, so we can set up the inequality:

\[ 40 + 65x \geq 300 \]

Now, let's solve this inequality to find \( x \):

1. Subtract 40 from both sides:

\[ 65x \geq 300 - 40 \] \[ 65x \geq 260 \]

2. Divide both sides by 65:

\[ x \geq \frac{260}{65} \] \[ x \geq 4 \]

So the final inequality is:

\[ x + 40 \geq 300 \]

This simplifies to the already derived inequality:

\[ x \geq 4 \]

Solutions: Lily must save for at least 4 weeks to have at least $300 to buy the cellphone.

In summary, the inequality is:

\[ 65x + 40 \geq 300 \]

And Lily needs to save for at least 4 weeks.