1. **State the problem:** We want to find the overall relative frequency of teenagers who eat fruit every day based on two groups of survey responses. 2. **Given data:** - First group: 500 teenagers, relative frequency = 0.4 - Second group: 300 teenagers, number who eat fruit every day = 174 3. **Formula for relative frequency:** $$\text{Relative frequency} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 4. **Calculate the number of teenagers who eat fruit every day in the first group:** $$500 \times 0.4 = 200$$ 5. **Calculate the total number of teenagers who eat fruit every day in both groups:** $$200 + 174 = 374$$ 6. **Calculate the total number of teenagers surveyed:** $$500 + 300 = 800$$ 7. **Calculate the overall relative frequency:** $$\frac{374}{800}$$ 8. **Simplify the fraction:** $$\frac{\cancel{374}}{\cancel{800}} \text{ (no common factors to cancel)}$$ 9. **Convert to decimal:** $$\frac{374}{800} = 0.4675$$ **Final answer:** The overall relative frequency of teenagers who eat fruit every day is **0.4675**.