The ratio of one-dollar coins to fifty-cent coins in a box was 3 : 4. 6 one-dollar coins were removed, and some fifty-cent coins of the same amount were added. The ratio of one-dollar coins to fifty-cent coins then became 1 : 3. What was the total amount of money in the box?
Let's assume that the initial number of one-dollar coins in the box is 3x, and the initial number of fifty-cent coins in the box is 4x.
The total value of the one-dollar coins is 3x * $1 = $3x.
The total value of the fifty-cent coins is 4x * $0.50 = $2x.
The initial total value of the money in the box is $3x + $2x = $5x.
After removing 6 one-dollar coins, the number of one-dollar coins becomes 3x - 6.
If the same number of fifty-cent coins are added, the number of fifty-cent coins becomes 4x + (3x - 6) = 7x - 6.
The new ratio of one-dollar coins to fifty-cent coins is 1 : 3, so we have the equation (3x - 6)/(7x - 6) = 1/3.
Cross-multiplying, we have 3(3x - 6) = 7x - 6.
Simplifying the equation, we get 9x - 18 = 7x - 6.
Combining like terms, we get 2x = 12.
Dividing both sides by 2, we get x = 6.
Substituting x = 6 back into the initial total value of the money in the box gives us $5x = $5 * 6 = $<<5*6=30>>30.
Therefore, the total amount of money in the box is $30. Answer: \boxed{30}.