The ratio of boys to girls in the choir was 5:4. Half of the boys left for practice which left 12 more girls than boys. How many students were in the choir before the boys left?

1 answer

Let the number of boys in the choir be represented as \(5x\) and the number of girls as \(4x\) based on the given ratio of boys to girls (5:4).

Half of the boys left for practice, so the number of boys remaining is:

\[ \frac{5x}{2} \]

After these boys left, it is stated that there were 12 more girls than boys left. This gives us the equation:

\[ 4x = \frac{5x}{2} + 12 \]

Next, we will eliminate the fraction by multiplying every term by 2:

\[ 2(4x) = 5x + 24 \]

This simplifies to:

\[ 8x = 5x + 24 \]

Now, we isolate \(x\) by subtracting \(5x\) from both sides:

\[ 8x - 5x = 24 \]

This results in:

\[ 3x = 24 \]

Now we divide both sides by 3:

\[ x = 8 \]

Now that we have the value of \(x\), we can find the numbers of boys and girls in the choir originally:

Number of boys:

\[ 5x = 5 \times 8 = 40 \]

Number of girls:

\[ 4x = 4 \times 8 = 32 \]

Now, to find the total number of students in the choir before any boys left:

\[ \text{Total} = 5x + 4x = 40 + 32 = 72 \]

Thus, the total number of students in the choir before the boys left is:

\[ \boxed{72} \]