SOLUTION: A group of women decided to contribute equal amounts toward obtaining a speaker for a book review. If there were 10 more women, each would have paid $2 less. However, if there were
Question 505738: A group of women decided to contribute equal amounts toward obtaining a speaker for a book review. If there were 10 more women, each would have paid $2 less. However, if there were 5 less women, each would have paid $2 more. How many women were in the group and how much was the speaker paid? Answer by Maths68(1474) (Show Source):
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Initially
Total number woman=x
Contribution for one woman = y
Total amount = x*y=xy
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After 5 did not join the group
Remaining women = x-5
Contribution for one woman = y+2
Total amount = (y+2)*(x-5)
Total amount = Total amount after 5 did not join the group
xy=(y+2)*(x-5)
xy=xy-5y+2x-10
0=-5y+2x-10
2x-5y-10=0
2x-5y=10…………..(1)
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After 10 more join the group
Total women = x+10
Contribution for one woman = y-2
Total amount = (y-2)*(x+10)
Total amount = Total amount after 10 more join the group
xy=(y-2)*(x+10)
xy=xy+10y-2x-20
0=10y-2x-20
-2x+10y-20=0
-2x+10y=20 ……………..(2)
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Add (1) and (2)
2x-5y=10…………..(1)
-2x+10y=20 ……………..(2)
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5y=30
Divide by 5 both sides of the equation
5y/5=30/5
y=6
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Put the value of y in (1)
2x-5y=10…………..(1)
2x-5(6)=10
2x-30=10
2x=10+30
2x=40
Divide by 2 both sides of the equation
2x/2=40/2
x=20
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Total number woman=x = 20
Total amount = xy=20*6=$120
Intial contribution for one woman = 120/20 = 6
After 5 did not join remaining women = 20-5=15
Contribution for one woman = 120/15 = 8
