Gaussville's soccer team won $40 \%$ of their first 40 games. They went on to win $n$ games in a row. At this point, they had won $50 \%$ of the total games they had played. What is the value of $n$ ?
(A) 4
(B) 10
(C) 12
(D) 8
(E) 9
Solution 1

Gaussville's soccer team won $40 \%$ of their first 40 games.

Thus they won $0.40 \times 40=16$ games.

After winning the next $n$ games in a row, they had won $16+n$ games and had played $40+n$ games.

At this point, they had won $50 \%$ or $\frac{1}{2}$ of their games.

This means that the number of games won, $16+n$, was $\frac{1}{2}$ of the number of games played, $40+n$. For which of the possible answers is $16+n$ equal to $\frac{1}{2}$ of $40+n$ ?

Substituting each of the five possible answers, we get that $16+8=24$ is $\frac{1}{2}$ of $40+8=48$, and so the value of $n$ is 8 .

## Solution 2

Gaussville's soccer team won $40 \%$ of their first 40 games.

Thus they had $0.40 \times 40=16$ wins and $40-16=24$ non-wins (losses or ties) in their first 40 games.

At this point, the team went on a winning streak which means they did not accumulate any additional non-wins.

Thus, their 24 non-wins represent $50 \%$ of the final total, and so the final number of wins is 24 . Therefore, Gaussville's soccer team won $n=24-16=8$ games in a row.

ANSWER: (D)