Question 1189654
<br>
Before plunging into a "standard" algebraic solution, take the time to analyze the problem to see if there is an easier way to set the problem up.<br>
At the start of the problem, Tony gave Peter 4/14=2/7 of his marbles; that means the number of marbles Tony started with was a multiple of 7. So<br>
Let 7x = # of marbles Tony started with.<br>
The number of marbles he gave to Peter was then 2x; the number Tony was left with was 5x.<br>
After Tony gave those marbles to Peter, the ratio of marbles the two of them had was 5:3.  So, since Tony finished with 5x marbles, Peter finished with 3x marbles.<br>
2x of the marbles Peter finished with were what Tony gave him; since Peter finished with 3x marbles, he started with x marbles.<br>
So Tony started with 7x marbles and Peter started with x marbles.<br>
ANSWER: The ratio of Peter's marbles to Tony's marbles at first was x:7x = 1:7<br>