Apply 7. Akira and Jen are competing to see who can sell the most tickets for the Winter Dance On Monday, Akira sold 20 and then sold 30 per day after that, Jen sold 50 on Monday and the sold 20 per day after that. This situation can be represented with the system \( y=30 x+20 \) a \( y=20 x+50 \), where \( x \) is the number of days after the first day, and \( y \) is the total tickets sol After how many days did they sell the same number of tickets?

To determine after how many days Akira and Jen will have sold the same number of tickets, let's analyze their sales using the given linear equations: - **Akira's Sales:** \( y = 30x + 20 \) - **Explanation:** Akira sold **20 tickets** on Monday (the first day) and then **30 tickets** each subsequent day. - **Jen's Sales:** \( y = 20x + 50 \) - **Explanation:** Jen sold **50 tickets** on Monday and then **20 tickets** each subsequent day. Here, \( x \) represents the number of days **after** the first day (Monday), and \( y \) represents the total number of tickets sold. **Step-by-Step Solution:** 1. **Set the Equations Equal to Each Other:** \[ 30x + 20 = 20x + 50 \] 2. **Solve for \( x \):** \[ 30x + 20 = 20x + 50 \] \[ 30x - 20x = 50 - 20 \] \[ 10x = 30 \] \[ x = 3 \] 3. **Interpret the Result:** - \( x = 3 \) means **3 days after Monday**. - Therefore, **on Thursday**, both Akira and Jen will have sold the same number of tickets. **Verification:** - **Akira's Sales on Day 3:** \[ y = 30(3) + 20 = 90 + 20 = 110 \text{ tickets} \] - **Jen's Sales on Day 3:** \[ y = 20(3) + 50 = 60 + 50 = 110 \text{ tickets} \] Both Akira and Jen sell **110 tickets** on the third day after Monday. **Conclusion:** Akira and Jen will have sold the same number of tickets **after 3 days**.