The question is in the description.

Question

If 12 more boys and 4 more girls join the school archery club, there will be 3 times as many boys as girls. If instead, 3 boys and 5 girls quit the club, there will be 7 times as many boys as girls. How many boys and girls are there in the club originally?

Answer 1

12 more boys and 4 more girls join the school archery club,

there will be 3 times as many boys as girls:

b + 12 = 3(g+4)

b + 12 = 3g + 12

b = 3g

 

3 boys and 5 girls quit the club, there will be

7 times as many boys as girls:

b-3 = 7(g-5)

b-3 = 7g - 35

b = 7g - 32

 

We already know that b = 3g so substitute that in:

3g = 7g - 32

4g = 32

g = 8

b = 3g = 24

 

There are 24 boys and 8 girls