The ratio of number of one-dollar coins to the number of fifty-cent coins in a box was 3:4. Six one-dollar coins were removed and some fifty-cent coins if the same amount were added. The ratio of the number of one-dollar coins to the number of fifty-cent coins to the number of fifty-cent then became 1:3. What was the total amount of money in the box?

Question

(3x-6)/(4x+6)=1/3

Answer 1

(3x-6)/(4x+12) = 1/3

it takes 12 fifty-cent coins to be "the same amount" as six dollar coins

Answer 2

number of $1 coins --- 3x
number of half-dollars --- 4x

Your second sentence does not make any sense to me

taking your equation ...
cross-multiply

9x - 18 = 4x+6
5x = 24
x = ???? , x must be a whole number

Fix your second sentence.