# Math

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There is a ratio of number of boys to girls 3:5. After adding 5 boys and 3 girls, the ratio become 5:7. How many girls were there at first?

• Math -

b = numbers of boys

g = numbers of girls

Ratio of boys to girls:

b / g = 3 / 5 Multiply both sides by 5

5 b / g = 3 Multiply both sides by g

5 b = 3 g Divide both sides by 5

b = 3 g / 5

( b + 5 ) / ( g + 3 ) = 5 / 7

[ ( 3 g / 5 ) + 5 ] / ( g + 3 ) = 5 / 7 Multiply both sides by 7

7 [ ( 3 g / 5 ) + 5 ] / ( g + 3 ) = 5 Multiply both sides by ( g + 3 )

7 [ ( 3 g / 5 ) + 5 ] = 5 ( g + 3 )

7 * 3 g / 5 + 7 * 5 = 5 ( g + 3 )
21 g / 5 + 35 = 5 ( g + 3 ) Multiply both sides by 5

21 g + 35 * 5 = 5 * 5 ( g + 3 )

21 g + 175 = 25 ( g + 3 )

21 g + 175 = 25 g + 25 * 3

21 g + 175 = 25 g + 75

175 - 75 = 25 g - 21 g

100 = 4 g

4 g = 100 Divide both sides by 4

g = 100 / 4

g = 25

b = 3 g / 5

b = 3 * 25 / 5

b = 75 / 5

b = 15

Checking :

b / g = 15 / 25 =

( 5 * 3 ) / ( 5 * 5 ) = 3 / 5

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

( 15 + 5 ) / ( 25 + 3 ) =

20 / 28 =

( 4 * 5 ) / ( 4 * 7 ) = 5 / 7

• Math -

Initial:

number of boys to girls 3:5
=3U:5U

U means unit
Later (3U +5): (5U +3) = 5:7

3U+5 5
----- = ---
5U+3 7

Cross multiply

21U+35 = 25U+15
35-15 = 25U-21U
20 = 4U
Therefore 1U =5

Initially girls are 5Units.

• Math -

My answer is also numbers of girls

g = 25

• Math -

Thanks a lot Bosnian.
Answer is exactly correct. Just wanted to provide the alternate method which got through Maths olympiad book.