SOLUTION: Hi - I got the answer to this by working it out but I cannot get to an equation. Can you help me? A class has a boy-girl ratio of 5:3. Three more girls join the class, changing

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Hi - I got the answer to this by working it out but I cannot get to an equation. Can you help me? A class has a boy-girl ratio of 5:3. Three more girls join the class, changing       Log On


   

Question 220420: Hi - I got the answer to this by working it out but I cannot get to an equation. Can you help me?
A class has a boy-girl ratio of 5:3. Three more girls join the class, changing the ratio of 10:7. How many students are now in the class?
By trying and just plugging in numbers I got 30 and 18 plus 3 more, so now the total is 51 - but I'm not sure how to set it up as a problem!
Thank you!
Found 2 solutions by scott8148, Theo:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
b / g = 5 / 3

"cross" multiplying ___ 3b = 5g ___ 6b = 10g

b / (g+3) = 10 / 7

7b = 10g + 30

substituting ___ 7b = 6b + 30 ___ b = 30

substituting ___ 3(30) = 5g ___ 90 = 5g ___ 18 = g

original class is 48 (30 + 18) ___ new class is 51 (48 + 3)

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
A class has a boy-girl ratio of 5:3. Three more girls join the class, changing the ratio of 10:7. How many students are now in the class?
By trying and just plugging in numbers I got 30 and 18 plus 3 more, so now the total is 51 - but I'm not sure how to set it up as a problem!
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let b = number of boys.
let g = number of girls.
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b/g = 5/3
this means that b = 5g/3
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add 3 girls and the ratio becomes 10/7
this means that:
b/(g+3) = 10/7
this means that:
b = (10g + 30)/7
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since both these equations equal to b, then they must equal to each other.
you get:
5g/3 = (10g + 30)/7
multiply both sides by 7 and you get:
35g/3 = 10g + 30
multiply both sides by 3 to get:
35g = 30g + 90
subtract 30g from both sides to get:
5g = 90
divide both sides by 5 to get:
g = 18
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original ratio led to bg = 5g/3
5*18/3 = 5*6 = 30
original class size is 30 boys and 18 girls.
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add 3 girls and the class size is 30 boys and 21 girls.
boy to girl ratio is now 30/21 which equals 10/7
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