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

Let b be the number of boys and g be the number of girls in the club originally.

From the first sentence, we have the system of equations:

b + 12 = 3(g + 4)
b = 3g + 8

From the second sentence, we have the system of equations:

b - 3 = 7(g - 5)
b = 7g - 32

We can solve for b in terms of g from both systems:

b = 3g + 8
b = 7g - 32

Setting the right-hand sides equal to each other, we get:

3g + 8 = 7g - 32

Solving for g, we get:

4g = 40

g = 10

Substituting g = 10 into either equation for b, we get:

b = 3g + 8 = 38

Therefore, there were originally 38 boys and 10 girls in the club.