SOLUTION: I'd appreciate your help sir/madam. I also tried my best answering this but I am really confused. A group of women decided to contribute equal amounts toward obtaining a speaker

Question 641684: I'd appreciate your help sir/madam.
I also tried my best answering this but I am really confused.
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?
Thanks a lot.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let a = total amt paid to the speaker
Let w = no. of women in the group
:
= amt paid by each woman
then
= amt paid by each if there were 10 more women
= amt paid by each if there were 5 less women
:
Write an equation for each scenario
5 less pd - actual pd = $2
- = 2
multiply by w(w-5) to clear the denominators:
aw - a(w-5) = 2w(w-5)
aw - aw + 5a = 2w^2 - 10w
5a = 2w^2 - 10W
and
actual pd - 10 more pd = $2
- = 2
multiply by w(w+10) to clear the fractions, resulting in
a(w+10) - aw = 2w(w+10)
aw + 10a - aw = 2w^2 + 20w
10a = 2w^2 + 20w
simplify, divide by 2
5a = w^2 + 10w
:
5a=5a so we can combine the two equations
2w^2 - 10w = w^2 + 10w
Combine on the left
2w^2 - w^2 - 10w - 10w = 0
w^2 - 20w = 0
Factor out w
w(w - 20) = 0
one reasonable solution
w = 20 women in the original group
:
Find the total amt paid (a)
5a = w^2 + 10w
replace w with 20
5a = 20^2 + 10(20)
5a = 400 + 200
5a = 600
a = 600/5
a = $120 paid to the speaker
;
;
:
Check this out
120/20 = $6 actually paid by each woman
120/30 = $4 paid (10 more women)
120/15 = $8 paid (5 women less)
:
I know there are a lot of steps here, I hope it made sense to you,
give it try anyway, to understand it. C
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