In a certain month a baseball team that played 60 games had won 30% of its games played. After a phenomenal winning streak this team raised its average to 50%. How many games must the team have won in a row to attain this average?

### Concept & Equation When a team goes on a winning streak, every consecutive win adds $+1$ to the number of games won AND $+1$ to the total number of games played. The new ratio must equal the new target percentage. $$\text{New Target } \% = \frac{\text{Initial Wins} + x}{\text{Initial Total Games} + x}$$ ### Step-by-Step Solution * **Initial State:** The team played 60 games and won 30%. $$\text{Initial Wins} = 30\% \text{ of } 60 = 0.3 \times 60 = 18$$ * **Winning Streak:** Let the number of consecutive games won be $x$. $$\text{New number of wins} = 18 + x$$ $$\text{New number of total games} = 60 + x$$ * **Setting up the Equation:** The new winning percentage is 50%, which is equivalent to $\frac{1}{2}$. $$\frac{18 + x}{60 + x} = \frac{1}{2}$$ * **Solve for $x$:** Cross-multiply to solve the linear equation. $$2(18 + x) = 1(60 + x)$$ $$36 + 2x = 60 + x$$ $$2x - x = 60 - 36$$ $$x = 24$$ ### Exam Strategy & Shortcut Use Option Elimination based on the 50% target. A 50% average means the total games played must be exactly double the number of games won. Let's test Option (c): 24 games. New wins = $18 + 24 = 42$. New total games = $60 + 24 = 84$. Is 42 exactly half of 84? Yes. The condition is satisfied instantly without writing out the algebra. ### Common Pitfall A very common mistake is adding the streak $x$ to the numerator (wins) but forgetting to add it to the denominator (total games). This results in the flawed equation $\frac{18 + x}{60} = 0.5 \implies x = 12$, which is explicitly placed as trap Option (a). ### Final Answer **Therefore, the correct answer is 24.**