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 ?

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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. 

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