The ratio of girls to boys 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 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

$$\boxed{{\displaystyle 36}}$$