SOLUTION: 4 men & 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

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Question 830688: 4 men & 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Man's rate, 1/y
Woman's rate , 1/x

4%281%2Fy%29%2B6%281%2Fx%29=1%2F8+
and
3%281%2Fy%29%2B7%281%2Fx%29=1%2F10

Simplify the first equation:
4/y+6/x=1/8, LCD 8xy
32x+48y=xy
Simplify the second equation:
3/y+7/x=1/10, LCD 10xy
30x+70y=xy

Find the system:
32x+48y=xy and 30x+70y=xy.
Subtracting the first one from the second one eliminates the xy term, member.
-2x+22y=0
-x+11y=0
highlight_green%2811y=x%29

Try substituting this in one of the equations of the system and use this to solve for y:
30x+70y=xy
30(11y)+70y=(11y)y
330y+70y=11y^2
400y=11y^2
11y^2-400y=0
highlight_green%28y%2811y-400%29=0%29
-
We can get a value for y from that. The y=0 is useless, but the 11y-400=0 gives highlight%28y=400%2F11%29;
Use this to find x.
-
30x+70y=xy
30x+79(400/11)=x(400/11)
(400/11)x-30x=79(400/11)
Multiply left and right by 11
400x-330x=79*400
70x=79*400
7x=79*40
x=79*40/7
highlight%28x=451%29, and y=36

How many days if just 10 women work?
10%281%2F451%29%2Ad=1 for the one job, d for how many days.
d=451%2F10
highlight%28d=45.1%29 days