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 \( \boxed{1:1} \).