Let the number of medals won by Sweden be \( S \), the number of medals won by China be \( C \), and the number of medals won by Germany be \( G \).
From the problem, we can set up the following equations based on the information given:
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Sweden won 3 medals more than China: \[ S = C + 3 \]
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Germany secured one more than twice the number of medals won by Sweden: \[ G = 2S + 1 \]
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The total number of medals won is 54: \[ S + C + G = 54 \]
Now we can substitute the expression for \( C \) from the first equation into the third equation. From \( S = C + 3 \), we can rearrange it to find \( C \): \[ C = S - 3 \]
Now substitute \( C \) in the total: \[ S + (S - 3) + G = 54 \] This simplifies to: \[ 2S - 3 + G = 54 \] \[ 2S + G = 57 \quad \text{(Equation 1)} \]
Next, substitute the expression for \( G \) from the second equation into Equation 1: \[ 2S + (2S + 1) = 57 \] \[ 4S + 1 = 57 \] Subtract 1 from both sides: \[ 4S = 56 \] Now divide by 4: \[ S = 14 \]
Now we can find \( C \) using \( C = S - 3 \): \[ C = 14 - 3 = 11 \]
Now, substituting \( S \) into the equation for \( G \): \[ G = 2S + 1 = 2(14) + 1 = 28 + 1 = 29 \]
Thus, the number of medals won by Germany is \( \boxed{29} \).
Lastly, let's verify the total:
- Sweden: \( S = 14 \)
- China: \( C = 11 \)
- Germany: \( G = 29 \)
Calculating the total: \[ S + C + G = 14 + 11 + 29 = 54 \]
The total is correct, confirming \( G = 29 \) is indeed the right answer.
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