We can start solving the problem by using algebra. Let x be the original number of one-dollar coins in the box, and y be the original number of fifty-cent coins. Then, based on the given information, we know that:
x:y = 3:4 (original ratio)
x-6:y+z = 1:3 (new ratio)
Where z is the number of fifty-cent coins added.
Now we can use the first equation to find x in terms of y.
x:y = 3:4
x = 3y/4
Now we can substitute x = 3y/4 into the second equation.
(3y/4 - 6) : (y + z) = 1:3
Now we can cross-multiply and simplify the equation to get:
3y/4 - 6 = y + z
3y - 8y = 12 + 4z
-5y = 12 + 4z
y = -12/5 - 4z/5
Now we can use this value of y to find the value of x.
x = 3y/4
x = 3(-12/5 - 4z/5) / 4
x = -9/5 - 3z/5
Now we can use the value of x and y to find the total amount of money in the box.
x + y = (-9/5 - 3z/5) + (-12/5 - 4z/5)
x + y = -21/5 - 7z/5
We know that the number of dollars is equal to the number of one dollar coin, the number of fifty cents is equal to the number of fifty-cent coins, so the total amount of money in the box is:
x + y = -21/5 - 7z/5 = -21/5100 - 7z/550 = -2100-35z
We don't know the value of z so we can't calculate the exact amount of money in the box.