Question

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 common factor.

1. Initial counts:

   • Box A: \( 3x \)
   • Box B: \( 5x \)

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

   • Amount transferred from A to B: \( \frac{1}{3} \times 3x = x \)
   • New counts:
     • Box A: \( 3x - x = 2x \)
     • Box B: \( 5x + x = 6x \)

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

   • Amount transferred from B to A: \( \frac{1}{3} \times 6x = 2x \)
   • New counts:
     • Box A: \( 2x + 2x = 4x \)
     • Box B: \( 6x - 2x = 4x \)

4. Final ratio of marbles:

   • The number of marbles in box A and box B is both \( 4x \).
   • The final ratio of the number of marbles in box A to the number of marbles in box B is:

\[ \frac{4x}{4x} = 1:1 \]

Thus, the ratio of the number of marbles in box A to the number of marbles in box B is \( \boxed{1:1} \).