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?

Answer 1

b = number of boys

g = number of girls

At first the ratio of the number of boys to the number of girls in a Mathematics Club was 1 : 2

b / g = 1 / 2

When 5 more boys joined the club , the ratio became 3 : 4

( b + 5 ) / g = 3 / 4

b / g = 1 / 2 Multiply both sides by 2

2 b / g = 1 Multiply both sides by g

2 b = g Divide both sides by 2

b = g / 2

( b + 5 ) / g = 3 / 4 Multiply both sides by 4

4 ( b + 5 ) / g = 3

( 4 b + 4 * 5 ) / g = 3

( 4 b + 20 ) / g = 3 Multiply both sides by g

4 b + 20 = 3 g

Replace b = g / 2 in equation 4 b + 20 = 3 g

4 b + 20 = 3 g

4 * g / 2 + 20 = 3 g

2 g + 20 = 3 g Subtract 2 g to both sides

2 g + 20 - 2 g = 3 g - 2 g

20 = g

g = 20

b = g / 2 = 20 / 2 = 10

10 boys and 20 girls