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

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

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