Briyana has \( \$ 150 \), and she needs to save at least \( \$ 560 \) for a spring break trip. If she can save \( \$ 45 \) per week, how long will it take her to save enough money? Let \( w \) = weeks saving money. Write an inequality to describe the situation. \( 45 w+150 \leq 560 \) \( 45 w+150 \geq 560 \) \( 150 w+45 \leq 560 \) \( 150 w+45 \geq 560 \) DONEIC

To determine how long Briyana needs to save to reach at least \$560 for her spring break trip, let's break down the problem step by step. ### Given: - **Initial Savings:** \$150 - **Weekly Savings:** \$45 per week - **Goal:** At least \$560 ### Let: - \( w \) = number of weeks Briyana needs to save ### Total Savings After \( w \) Weeks: \[ \text{Total Savings} = \text{Initial Savings} + (\text{Weekly Savings} \times \text{Number of Weeks}) \] \[ \text{Total Savings} = 150 + 45w \] ### Setting Up the Inequality: Since Briyana needs **at least** \$560, the total savings should be **greater than or equal to** \$560. \[ 150 + 45w \geq 560 \] ### Explanation of the Options: 1. **\( 45w + 150 \leq 560 \)** - This implies that her savings should be **less than or equal to** \$560, which is not the goal. 2. **\( 45w + 150 \geq 560 \)** - This correctly represents that her savings should be **greater than or equal to** \$560. 3. **\( 150w + 45 \leq 560 \)** - This incorrectly multiplies the initial savings by weeks and adds a fixed \$45, which doesn't align with the problem. 4. **\( 150w + 45 \geq 560 \)** - Similar to option 3, this incorrectly structures the equation. ### Conclusion: The correct inequality that describes the situation is: \[ 45w + 150 \geq 560 \] This inequality ensures that after \( w \) weeks of saving \$45 each week, along with her initial \$150, Briyana will have **at least** \$560. **Answer:** \( 45w + 150 \geq 560 \)