1. **State the problem:** Mr. Chain has apples where 3 out of 4 are red and the rest are green. He sold half of the total apples. Of the apples sold, 5 out of 6 were red. After selling, 28 green apples remain. We need to find how many red apples Mr. Chain sold. 2. **Define variables:** Let the total number of apples be $T$. 3. **Express red and green apples:** - Red apples: $\frac{3}{4}T$ - Green apples: $\frac{1}{4}T$ 4. **Apples sold:** Half of total apples sold, so apples sold = $\frac{T}{2}$. 5. **Red apples sold:** $\frac{5}{6}$ of apples sold are red, so red apples sold = $\frac{5}{6} \times \frac{T}{2} = \frac{5T}{12}$. 6. **Green apples sold:** The rest of the sold apples are green, so green apples sold = $\frac{T}{2} - \frac{5T}{12} = \frac{6T}{12} - \frac{5T}{12} = \frac{T}{12}$. 7. **Green apples left:** Total green apples minus green apples sold equals green apples left: $$\frac{1}{4}T - \frac{T}{12} = 28$$ 8. **Simplify the left side:** $$\frac{3T}{12} - \frac{T}{12} = \frac{2T}{12} = \frac{T}{6}$$ So, $$\frac{T}{6} = 28$$ 9. **Solve for $T$:** $$T = 28 \times 6 = 168$$ 10. **Find red apples sold:** $$\frac{5T}{12} = \frac{5 \times 168}{12} = \frac{840}{12} = 70$$ **Final answer:** Mr. Chain sold 70 red apples.