At first the ratio of the number of boys to the number of girls in a Mathematics Club was I : 2 when 5 more boys joined the club, the ratio became 3 : 4 How many members were there in the club at first?

X=number of boys in the club at first

y=number of girls in the club at first.

(x+y) = members were in the club at first.

We can suggest the next system of equation.

x/y=1/2 ⇒ x=y/2

(x+5) / y=3/4 ⇒4 (x+5) = 3y

Finally, we have the next system of equations:

x=y/2

4 (x+5) = 3y

We are going to solve by substitution method.

4 (y/2 + 5) = 3y

2y+20=3y

2y-3y=-20

-y=-20

y=20

x=y/2

x=20/2

x=10

(x+y) = 10+20=30

Answer: There were 30 members int the club at first, they were 10 boys and 20 girls.