Question

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?

Answer 1

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:

\[
\boxed{72}
\]