# Math

posted by .

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.

## Similar Questions

1. ### Math

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. 20 girls, 35 boys B. 24 girls, 36 boys
2. ### math

The ratio of boys to girls in a school choir is 4:3. There are 6 more boys than girls. If another 2 girls join the choir, what will be the new ratio of boys to girls?
3. ### math !!!! :O

The ratio of boys to girls in a school choir is 4:3. There are 6 more boys than girls. If another 2 girls join the choir, what will be the new ratio of boys to girls?
4. ### math

The ratio of boys to girls in a school choir is 4:3. There are 6 more boys than girls. If another 2 girls join the choir, what will be the new ratio of boys to girls?
5. ### Math

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?
6. ### Math

If the ratio of girls to boys on the track team is 5 to 6 which of these shows possible numbers of girls to boys on the track team?
7. ### math

300 hundred kids attend a dance. The ratio of boys to girls is 6 to 4. If 30 boys and 20 girls leave, what is the new ratio of boys to girls still at the dance
8. ### Math

Students surveyed boys and girls separately to determine which sport was enjoyed the most. After completing the boy survey, it was determined that for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball. The girl survey had …
9. ### math

At a sports carnival,the ratio of number of pupils sent by school A,B and school C to the event was 1:2:3. The number of boys from school A and the number of girls from school B were the same. The ratio of the number of girls from …
10. ### Math

Which table correctly fills in the ratio table below?

More Similar Questions