There are 2 girls and 6 boys playing a game. How many additional girls must join the game so that $\frac{5}{8}$ of the players are girls?
(A) 6
(B) 3
(C) 5
(D) 8
(E) 7

Part B: Each correct answer is worth 6.
Solution 1

When $\frac{5}{8}$ of the players are girls then $\frac{3}{8}$ of the players will be boys. Since the number of boys playing is 6 (and does not change), then after the additional girls join, there must be 16 players in total for $\frac{3}{8}$ of the players to be boys. Since there were 8 players initially, then 8 additional girls must have joined the game.

## Solution 2

Let the number of additional girls be $g$.

Then

$$
\begin{aligned}
\frac{2+g}{8+g} & =\frac{5}{8} \\
16+8 g & =40+5 g \\
3 g & =24 \\
g & =8
\end{aligned}
$$