The ratio of the number of marbles in box A to the number of marbles in box B is 3:5. If 1/3 of the marbles in box A is transfered to box B and then 1:3 of the marbles in box B is transferesnto box A what will be the ratio of the number of marbles im box A to the number od marbles im box B. (Express your answer in the simplest form?)

Answer 1

Let the number of marbles in box A be \( 3x \) and the number of marbles in box B be \( 5x \), where \( x \) is a positive integer.

1. Transfer 1/3 of the marbles from box A to box B:

   • The number of marbles transferred from box A to box B is: \[ \frac{1}{3} \times 3x = x \]
   • After the transfer:
     • Box A: \( 3x - x = 2x \)
     • Box B: \( 5x + x = 6x \)

2. Transfer 1/3 of the marbles from box B back to box A:

   • The number of marbles transferred from box B to box A is: \[ \frac{1}{3} \times 6x = 2x \]
   • After the transfer:
     • Box A: \( 2x + 2x = 4x \)
     • Box B: \( 6x - 2x = 4x \)

3. Calculate the ratio of the number of marbles in box A to the number of marbles in box B:

   • The ratio is: \[ \frac{4x}{4x} = 1 \]

Thus, the final ratio of the number of marbles in box A to the number of marbles in box B is 1:1.