Step 1a

The ratio of boys to girls in the choir is 24:36. This means that for every 24 boys, there are 36 girls. Since there are 12 more boys than girls, we can represent this as: 24x = 36x - 12

Where "x" is a common multiplier to find the actual numbers of boys and girls. Now, let’s solve for "x":

24x = 36x - 12

12x = 12

x = 1

So, there is 1 set of 24 boys and 36 girls in the choir.

Explanation: There is one set of 24 boys and 36 girls in the choir, and we have found the value of x.

Step 1b

Now, if 6 more girls join the choir, the number of girls will increase to 36 + 6 = 42. The number of boys remains the same at 24.

The new ratio of boys to girls will be 24:42. Now, simplify the ratio by dividing both parts by their greatest common factor, which is 6:

24 ÷ 6 = 4

42 ÷ 6 = 7

So, the new simplified ratio of boys to girls is 4:7.

Explanation: Therefore, the new ratio of boys to girls after 6 more girls join the choir is 4:7.