Let the number of girls in the choir be represented as \( 5x \) and the number of boys as \( 4x \), given the ratio of girls to boys as \( 5:4 \).
When half of the boys left for practice, the number of boys remaining would be:
\[ \text{Remaining boys} = \frac{4x}{2} = 2x \]
According to the problem, after half of the boys left, there were 12 more girls than boys remaining. We can express this relationship mathematically as:
\[ 5x = 2x + 12 \]
Now, we will solve for \( x \). First, subtract \( 2x \) from both sides:
\[ 5x - 2x = 12 \] \[ 3x = 12 \]
Next, divide by 3:
\[ x = 4 \]
Now that we have found \( x \), we can calculate the number of girls and boys in the choir:
\[ \text{Number of girls} = 5x = 5 \times 4 = 20 \] \[ \text{Number of boys} = 4x = 4 \times 4 = 16 \]
Now, we need to find the total number of students in the choir:
\[ \text{Total students} = \text{Number of girls} + \text{Number of boys} = 20 + 16 = 36 \]
Thus, the total number of students in the choir before the boys left is
\[ \boxed{36} \]
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