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 set up the inequality, we start with the amount Lily currently has from her grandfather, which is $40, and we add the amount she earns each week, which is $65 times the number of weeks she saves, represented by \( x \).

The total amount of money Lily needs is at least $300, so we can write the inequality as follows:

\[ 40 + 65x \geq 300 \]

Now, let's solve for \( x \):

1. Subtract 40 from both sides:

   \[ 65x \geq 300 - 40 \]

   \[ 65x \geq 260 \]

2. Divide both sides by 65:

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

   \[ x \geq 4 \]

Thus, the inequality is:

\[ x + 4 \geq 300 \]

This can be rewritten in the specified format as:

\[ x \geq 4 \]

Solution Description:

Lily must save for at least 4 weeks to have at least $300. This means that if she saves for 4 weeks or more, she will reach her goal of $300 or more, allowing her to buy the cellphone. Any value of \( x \) that is 4 or greater (e.g., 4, 5, 6, ...) satisfies the requirement.