1. **State the problem:** Tom has 80 more game cards than Ken originally. After Tom gives 100 cards to Ken, Tom's cards become 0.6 times Ken's cards. We need to find the total number of cards they originally had. 2. **Define variables:** Let $T$ = number of cards Tom originally had. Let $K$ = number of cards Ken originally had. 3. **Write equations from the problem:** From the first statement: $$T = K + 80$$ After Tom gives 100 cards to Ken: Tom's cards: $T - 100$ Ken's cards: $K + 100$ From the second statement: $$T - 100 = 0.6(K + 100)$$ 4. **Substitute $T$ from the first equation into the second:** $$K + 80 - 100 = 0.6(K + 100)$$ Simplify left side: $$K - 20 = 0.6K + 60$$ 5. **Solve for $K$:** $$K - 0.6K = 60 + 20$$ $$0.4K = 80$$ $$K = \frac{80}{0.4}$$ $$K = 200$$ 6. **Find $T$ using $T = K + 80$:** $$T = 200 + 80 = 280$$ 7. **Find total cards originally:** $$T + K = 280 + 200 = 480$$ **Final answer:** The total number of game cards originally owned by Tom and Ken is **480**.