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 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**.