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Let's work through these two problems one by one.

### Problem 4:
- **Alethea** plants 3 rows of carrots for every 4 rows of pepper plants.
- **Tommie** plants 2 rows of carrots for every 1 row of pepper plants.
- Alethea plants 9 rows of carrots.
- Tommie plants twice that amount, meaning Tommie plants \( 9 \times 2 = 18 \) rows of carrots.

**Step 1: Determine how many rows of pepper plants Alethea plants.**
- Alethea's ratio of carrots to pepper plants is 3:4. If she plants 9 rows of carrots, we need to find how many rows of pepper plants she plants.
  \[
  \text{Pepper plants} = \left(\frac{4}{3}\right) \times 9 = 12 \text{ rows of pepper plants}.
  \]

**Step 2: Determine how many rows of pepper plants Tommie plants.**
- Tommie's ratio of carrots to pepper plants is 2:1. If Tommie plants 18 rows of carrots, we can find how many rows of pepper plants are planted.
  \[
  \text{Pepper plants} = \left(\frac{1}{2}\right) \times 18 = 9 \text{ rows of pepper plants}.
  \]

**Conclusion:** Alethea plants more rows of pepper plants (12 rows) than Tommie (9 rows).

---

### Problem 5:
- **John** hits the center 1 time for every 3 arrows.
- **Ryan** hits the center 2 times for every 5 arrows.
- Both boys have 30 arrows, and they need to hit the center **more than 10 times** to earn their merit badge.

**Step 1: Calculate how many times John hits the center.**
- For every 3 arrows, John hits the center once. So, for 30 arrows:
  \[
  \text{John's hits} = \left(\frac{1}{3}\right) \times 30 = 10 \text{ hits}.
  \]
- John hits exactly 10 times, so he does **not** earn the merit badge (since he must hit more than 10 times).

**Step 2: Calculate how many times Ryan hits the center.**
- For every 5 arrows, Ryan hits the center twice. So, for 30 arrows:
  \[
  \text{Ryan's hits} = \left(\frac{2}{5}\right) \times 30 = 12 \text{ hits}.
  \]
- Ryan hits 12 times, so he **does** earn the merit badge.

**Conclusion:** **Ryan** earns the archery merit badge, but John does not.

---

Would you like more details on these steps or any further clarification?

### Related Questions:
1. How would the answer change if Tommie planted a different number of carrot rows in Problem 4?
2. What if Alethea's ratio of carrots to pepper plants changed—how would that affect the comparison?
3. How many arrows would John need to hit the center more than 10 times in Problem 5?
4. What would happen if Ryan's hit ratio changed to 3 hits for every 7 arrows?
5. Could both boys earn their merit badges if the number of arrows was reduced to 15? Why or why not?

**Tip:** When working with ratios, always ensure you correctly match corresponding quantities in the ratio and scale them appropriately.

4. Tommie and Alethea plant a summer garden in their backyard. Alethea plants 3 rows of carrots for every 4 rows of pepper plants. Tommie plants 2 rows of carrots for every 1 row of pepper plants. If Alethea plants 9 rows of carrots and Tommie plants twice that amount, who plants more rows of pepper plants?

5. Summer campers John and Ryan are trying to earn their archery merit badges. Each boy has 30 arrows and must hit the center of the target more than 10 times. John hits the center 1 time for every 3 arrows he shoots. Ryan hits the center 2 times for every 5 arrows he shoots. Which boy earns an archery merit badge?

Learn how to solve problems involving ratios and proportions with detailed steps. Understand how Alethea and Tommie compare their garden plantings and determine who plants more rows of pepper plants. Discover whether John or Ryan earns an archery merit badge by calculating their target hits. Suitable for students in Grades 5-7.

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