SOLUTION: I think I know the answer but can't get the formula right. HELP!!! From a group of boys and girls, fifteen girls leave. Twice as many boys as girls are left. Then forty-five boy

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I think I know the answer but can't get the formula right. HELP!!! From a group of boys and girls, fifteen girls leave. Twice as many boys as girls are left. Then forty-five boy      Log On


   

Question 30524: I think I know the answer but can't get the formula right. HELP!!!
From a group of boys and girls, fifteen girls leave. Twice as many boys as girls are left. Then forty-five boys leave. Five times as many girls as boys remain. How many boys and girls were in the initial group?
Found 2 solutions by josmiceli, checkley71:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
b= initial number of boys
g = initial number of girls
when 15 girls leave, there are twice as many boys as girls
b = 2(g-15)
45 boys leave, 5 times as many girls remain
5(b-45) = g - 15
5b -225 = g - 15
from above
b/2 = g - 15
substitute
5b - 225 = b/2
10b -450 = b
9b = 450
b = 50
50/2 = g - 15
g = 25 + 15
g = 40
check
initially
b = 50
g = 40
15 girls leave
b = 50
g = 25
there are twice as many boys as girls
45 boys leave
b = 5
g = 25
five times as many girls remain
checks OK

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
2G=B-15 OR B=2G+15
G=5(B-15-45) OR G=5((2G+15)-15-45) OR G=5(2G+15-15-45) OR G=5(2G+30-30-45) OR
G=5(2G-45) OR G=10G-225 OR 225=9G OR 225/9=G OR 25=GIRLS
B=2X25+15 OR B=50+15 OR BOYS=65.