Final answer:
To improve the win rate from 48% to 60%, 8 games need to be played.
Step-by-step explanation:
To improve the win rate from 48% to 60%, we need to find the number of games won out of the total games played. Let x be the number of games needed to improve the win rate to 60%. We can set up the following equation: 12 + x / 25 + x = 0.60. Solving this equation will give us the number of games that need to be played to achieve a 60% win rate.
Cross multiplying, we get 12 + x = 0.60(25 + x). Simplifying, we get 12 + x = 15 + 0.60x. Subtracting 0.60x from both sides, we get 0.40x = 3. Subtracting 12 from both sides, we get x = 7.5. Since we can't have half a game, we round up to the nearest whole number. Therefore, 8 games need to be played to improve the win rate to 60%.