1. **State the problem:** A store has 3 types of accessories: scarves, ties, and belts. Scarves are 20%, ties are 60%, and belts are 40 items. Half of the ties are replaced with scarves. We need to find the new number of scarves. 2. **Define variables and total:** Let the total number of accessories be $T$. 3. **Express quantities:** - Scarves: $0.20T$ - Ties: $0.60T$ - Belts: 40 4. **Write total equation:** $$0.20T + 0.60T + 40 = T$$ 5. **Simplify:** $$0.80T + 40 = T$$ 6. **Isolate $T$:** $$T - 0.80T = 40$$ $$\cancel{T} - 0.80\cancel{T} = 40$$ $$0.20T = 40$$ 7. **Solve for $T$:** $$T = \frac{40}{0.20} = 200$$ 8. **Calculate original scarves and ties:** - Scarves: $0.20 \times 200 = 40$ - Ties: $0.60 \times 200 = 120$ 9. **Half of ties replaced with scarves:** - Half ties: $\frac{120}{2} = 60$ - New scarves: original scarves + half ties replaced $$40 + 60 = 100$$ **Final answer:** The store will have **100 scarves** after the replacement.