Tony and Peter both had some marbles at first. After Tony gave Peter 4/14 of his marbles, the ratio of Tony's marbles to Peter's marbles became 5:3. What was the ratio of Peter's marbles to Tony's marbles at first?

Answer 1

Let's assume that Tony had T marbles at first and Peter had P marbles at first.
After Tony gave Peter 4/14 of his marbles, Tony had T - (4/14)T = (10/14)T marbles left.
The ratio of Tony's marbles to Peter's marbles became 5:3, so (10/14)T / P = 5/3
Cross multiplying, we get (10/14)T = (5/3)P
Simplifying, we get (5/7)T = (5/3)P
Dividing both sides by (5/3), we get T = (7/3)P
Therefore, the ratio of Peter's marbles to Tony's marbles at first was P/T = P / ((7/3)P) = 3/7. Answer: \boxed{3:7}.