SOLUTION: the ratio of boys to girls in a group is 3:4. if 6 more boys join the group and 6 girls leave the group the ratio becomes 4:3. How many girls were originally in the group?

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Question 1175686: the ratio of boys to girls in a group is 3:4. if 6 more boys join the group and 6 girls leave the group the ratio becomes 4:3. How many girls were originally in the group?
Found 3 solutions by MathLover1, MathTherapy, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
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let the number of boys be b and the number of girls be g

b%2Fg=3%2F4
b=3g%2F4.....eq.1
%28b%2B6%29%2F%28g-6%29=4%2F3
b%2B6=4%28g-6%29%2F3
b%2B6=%284g-24%29%2F3
b%2B6=4g%2F3-8
b=4g%2F3-8-6
b=4g%2F3-14.....eq.2
from eq.1 and eq.2 we have
3g%2F4=4g%2F3-14
14=4g%2F3-3g%2F4
14=16g%2F12-9g%2F12
14=7g%2F12
7g=14%2A12
g=14%2A12%2F7
g=2%2A12
g=24
go to
b=3g%2F4.....eq.1, substitute g
b=%283%2A24%29%2F4
b=3%2A6%7D+%7D%7D%0D%0A%7B%7B%7Bb=18

so, 24girls were originally in the group


Answer by MathTherapy(10552) About Me  (Show Source):
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the ratio of boys to girls in a group is 3:4. if 6 more boys join the group and 6 girls leave the group the ratio becomes 4:3. How many girls were originally in the group? 
Let multiplicative factor be x

Then original number of boys and girls = 3x, and 4x, respectively

Then we get: matrix%281%2C3%2C+%283x+%2B+6%29%2F%284x+-+6%29%2C+%22=%22%2C+4%2F3%29

3(3x + 6) = 4(4x - 6) ------ Cross-multiplying

9x + 18 = 16x - 24

9x - 16x = - 24 - 18

- 7x = - 42

Multiplicative factor, or matrix%281%2C5%2C+x%2C+%22=%22%2C+%28-+42%29%2F%28-+7%29%2C+%22=%22%2C+6%29

Original number of girls: 

That's all! Nothing MORE, nothing LESS!!

Answer by greenestamps(13200) About Me  (Show Source):
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Note to the student:

Tutor @Math Therapy started on the problem by letting the numbers of boys and girls be 3x and 4x.

The other tutor started on the problem by saying that the number of boys is 3/4 the number of girls.

Compare the amount of work involved in solving the problem by the two methods; the first method requires FAR less work.

You should learn from this that VIRTUALLY ALWAYS (if not always) the best way to start work on a problem when given a ratio like 5:7 is to let the two numbers be 5x and 7x.