Question 265919: From a group of green monkeys, 10 females leave. At this point there are 3 males for every female. Then 25 males leave, at which point there are two males for every female. How many females were there originally?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! OK.
Let x=number of female green monkeys in the original group
And let y=number of male green monkeys in the original group
Then (x+y)=total number of monkeys in the original group
When 10 female green monkeys leave, we have left (x-10)+y monkeys remaining and we are basically told that 3/4 of this number are males, so:
(3/4)((x-10)+y)=y multiply each side by 4
3((x-10)+y)=4y get rid of parens
3x-30+3y=4y subtract 4y and add 30 to each side
3x-30+30+3y-4y=4y-4y+30 collect like terms
3x-y=30-----------------------------------------eq1
When 25 males leave, we have left(x-10)+(y-25) or (x+y-35) monkeys remaining and we are told that 2/3 of this number are males, so:
(2/3)(x+y-35)=(y-25) multiply each side by 3
2(x+y-35)=3(y-25) get rid of parens
2x+2y-70=3y-75 subtract 3y and add 70 to each side
2x+2y-70+70-3y=3y-3y-75+70 collect like terms
2x-y=-5----------------------------------------eq2
subtract eq2 from eq1 and we get
x=35------------------------------number of females originally
substitute x=35 into eq 1 and we get:
3*35-y=30
105-y=30
-y=-105+30=-75
y=75 number of males originally
CK
10 females leave:
Number of females remaining:35-10=25
Number of males: 75
Total number of monkeys: 75+25=100
75/100=3/4
3/4=3/4
25 males leave:
Number of females remaining=25
Number of males=75-25=50
Total number of monkeys=50+25=75
50/75=2/3
2/3=2/3
Hope this helps---ptaylor
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