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?

This question still have no answer summary yet.

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.

So the answer is 25.

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.

So the answer is 25.

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

After adding ratio is :

( 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

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

After adding ratio is :

( 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

is exactly correct. Just wanted to provide the alternate method which got through Maths olympiad book.

Did this answer your question? If not, ask a new question.

- If the ratio of girls to boys on the swim team is 2:3, which of these shows the possible number of girls to boys:A
If the ratio of girls to boys on the swim team is 2:3, which of these shows the ...

- in class of x students, when 2 more boys and 7 more girls are added, the ratio of boys to girls change from 2/3 to 3/5
in class of x students, when 2 more boys and 7 more girls are added, the ratio o...

- there are 15 girls and 12 boys in math class. express the ratio of boys and girls in simplest...
there are 15 girls and 12 boys in math class. express the ratio of boys and girl...

- There is a ratio of number of boys to girls 3:5
There is a ratio of number of boys to girls 3:5...

- If girls made “A’s” on a ratioof 7 to 5 compared to boys(of course this is not in ourschool), how many “A’s” would the boys make, if the girls made 92
If girls made “A’s” on a ratioof 7 to 5 compared to boys(of course this is...

- Ratio of boys to girls
Ratio of boys to girls...

- The ratio of girls to boys in Mr
The ratio of girls to boys in Mr...

- The ratio of boys to girls in Mr
The ratio of boys to girls in Mr...

- The ratio of boys to girls in Mr
The ratio of boys to girls in Mr...

- The ratio of girls to boys in a particular classroom is 6:5
The ratio of girls to boys in a particular classroom is 6:5...