SOLUTION: here is my question- a group of women decide to contribute equal amounts toward obtaining a speaker for a book review. If there were 10 more women, each would have paid $2 less. Ho

Question 472802: here is my question- a group of women decide 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?
If you can, could you also show me how you did it?
Thanks!
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
a group of women decide 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?
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Let A = the amount the speaker was paid
Let a = the amount each woman paid
Let n = the number of women in the group
Given the information above, we can write the following 3 equations:
A = na
A = (n+10)(a-2)
A = (n-5)(a+2)
Since the LHS's are equal we can write:
na = (n+10)(a-2) [1]
na = (n-5)(a+2) [2]
Now we are left with 2 equations and 2 unknowns. Solving for a in [1] gives:
na = na - 2n + 10a - 20 -> 2n = 10a - 20 -> n = 5a - 10
Now simplify [2] and substitute in this value for n:
na = na + 2n - 5a - 10 -> 2n - 5a - 10 = 0 -> 2(5a - 10) - 5a - 10 = 0
Solving for a gives:
10a - 20 - 5a - 10 = 0
5a - 30 = 0
This gives a = 6
Therefore, n = 5*6 - 10 -> n = 20
So there were 20 women in the group and the speaker was paid 20*6 = $120

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