Question 472802
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