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.

Question

______ x + ______ ≥ _________, where x is the number of weeks Lily will need to save.

Answer 1

To write the inequality for the number of weeks Lily will need to save, we can start by determining how much money she has initially and how much she will earn each week.

1. Initial amount from her grandfather: $40
2. Amount earned per week: $65
3. Total amount needed to buy the phone: $300

We can represent the total amount Lily will have after saving for \( x \) weeks as the sum of her initial amount and her weekly earnings:

\[ 40 + 65x \]

To find out when this amount will be at least $300, we can set up the following inequality:

\[ 40 + 65x \geq 300 \]

This inequality represents the number of weeks \( x \) she needs to save in order to have at least $300 for the cellphone.

So, the completed inequality is:

65 x + 40 ≥ 300.

Answer 2

Solve the inequality you wrote above. What is the minimum amount of weeks she will need to save in order to buy the new phone?

Answer 3

To solve the inequality:

\[ 40 + 65x \geq 300 \]

we can follow these steps:

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 minimum number of weeks Lily will need to save in order to buy the new phone is 4 weeks.