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

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)
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 ≥
, where x
 is the number of weeks Lily will need to save. Lily must save for at least 
 weeks to have at least $300.

GPT-4o mini · Answer

To write an inequality for the number of weeks Lily will need to save, we start with the amount she has and the amount she will earn.

Lily starts with $40 from her grandfather and earns $65 each week tutoring. We want her total savings to be at least $300.

Let $ x $ represent the number of weeks Lily saves. The total amount she will have after $ x $ weeks can be represented as:

\[ 40 + 65x \]

We want this total to be at least $300, so we can set up the inequality:

\[ 40 + 65x \geq 300 \]

Now, to find the minimum number of weeks $ x $ she needs to save, we can solve the inequality:

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 complete inequality is:

\[ 40 + 65x \geq 300 \]

Lily must save for at least 4 weeks to have at least $300. The solutions for $ x $ (the number of weeks) are all whole numbers $ x $ that are 4 or greater. This means she can save for 4 weeks, 5 weeks, or any number of weeks greater than 4 to reach her savings goal.