SOLUTION: when 6 new boys were admitted and 6 girls left from the class, the percentage of girls decreased from 68% to 56%. find the original number of boys and girls in the class

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: when 6 new boys were admitted and 6 girls left from the class, the percentage of girls decreased from 68% to 56%. find the original number of boys and girls in the class      Log On


   

Question 989156: when 6 new boys were admitted and 6 girls left from the class, the percentage of girls decreased from 68% to 56%. find the original number of boys and girls in the class
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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when 6 new boys were admitted and 6 girls left from the class, the percentage of girls decreased from 68% to 56%. find the original number of boys and girls in the class
:
let g = original number of girls
let b = original number of boys
then
(g+b) = total in the class
:
First equation
g%2F%28g%2Bb%29 = .68
g = .68(g+b)
g = .68g + .68b
g - .68g = .68b
.32g = .68b
g = %28.68b%29%2F.32
g = 2.125b
:
Second equation
Adding 6 boys and subtracting 6 girls, class total is the same
%28g-6%29%2F%28g%2Bb%29 = .56
g - 6 = .56(g+b)
g - 6 = .56g + .56b
g - .56g = .56b + 6
.44g = .56b + 6
Replace g with 2.125b
.44(2.125b) = .56b + 6
.935b - .56b = 6
.375b = 6
b = 6/.375
b = 16 boys originally
:
Find the girls
g = 2.125(16)
g = 34 girls originally
:
;
See if this checks out, total is 16 + 34 = 50
34/50 = .68
and 6 less girls
28/50 = .56