<PRE><B>Question 1187372</B>
&lt;br&gt;
It&#39;s interesting that the other tutor showed one way to set up the problem and didn&#39;t follow through to the solution.  In fact, a solution starting with the way they set up the problem is awkward; no doubt that was why they didn&#39;t finish the problem.&lt;br&gt;
I would solve the problem in a completely different way, starting with the given ratios for the number each of them had at the end.  At the end...&lt;br&gt;
S:T = 4:3
S:J = 3:2&lt;br&gt;
Rewrite those two ratios as equivalent ratios, where the numbers for Sandra in the two ratios are the same:&lt;br&gt;
S:T = 12:9
S:J = 12:8&lt;br&gt;
Then&lt;br&gt;
S:T:J = 12:9:8&lt;br&gt;
Using that, let the numbers they had at the end be
Sandra = 12x
Ted = 9x
Justina = 8x&lt;br&gt;
The total number of coins is the same at the end as the beginning:&lt;br&gt;
12x+9x+8x=377
29x=377
x=377/29=13&lt;br&gt;
So the numbers each had at the end were (S,T,J) = (12x,9x,8x) = (156,117,104)&lt;br&gt;
In the second exchange, Ted received 13 coins from Justina.  So before that exchange Justina had 13 more than at the end and Ted had 13 fewer than at the end: (S,T,J) = (156,104,117)&lt;br&gt;
In the first exchange, Sandra gave Justina 15 coins.  So before that exchange Justina had 15 fewer coins and Sandra had 15 more coins: (S,T,J) = (171,104,102)&lt;br&gt;
ANSWER: In the beginning, Sandra had 171 coins, Ted had 104, and Justina had 102.&lt;br&gt;
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