SOLUTION: Hi Sandra ted and Justina had a total of 377 coins. Sandra gave justina 15 coins and ted received 13 coins from justina. In the end the ratio of the number of coins that sandra an

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Question 1187372: Hi
Sandra ted and Justina had a total of 377 coins. Sandra gave justina 15 coins and ted received 13 coins from justina. In the end the ratio of the number of coins that sandra and ted had was 4:3 respectively and the ratio of the number of coins that Sandra and justina had was 3:2 respectively. How many coins did each have at first.
Thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                Sandra           Ted            Justina
total            x               t               j                     377
first xfers      x-15            t+13           j+15-13=j+2


system%28%28x-15%29%2F%28t%2B13%29=4%2F3%2C%28x-15%29%2F%28j%2B2%29=3%2F2%29

system%283%28x-15%29=4%28t%2B13%29%2C2%28x-15%29=3%28j%2B2%29%29
also x%2Bt%2Bj=377

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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


It's interesting that the other tutor showed one way to set up the problem and didn'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't finish the problem.

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...

S:T = 4:3
S:J = 3:2

Rewrite those two ratios as equivalent ratios, where the numbers for Sandra in the two ratios are the same:

S:T = 12:9
S:J = 12:8

Then

S:T:J = 12:9:8

Using that, let the numbers they had at the end be
Sandra = 12x
Ted = 9x
Justina = 8x

The total number of coins is the same at the end as the beginning:

12x+9x+8x=377
29x=377
x=377/29=13

So the numbers each had at the end were (S,T,J) = (12x,9x,8x) = (156,117,104)

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)

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)

ANSWER: In the beginning, Sandra had 171 coins, Ted had 104, and Justina had 102.