SOLUTION: A group of small business owners pledge a total of 1,000 a month to beautify the mall. The owners agreed to split the cause equally. When 5 went out of business, the rest had to pa

Question 663702: A group of small business owners pledge a total of 1,000 a month to beautify the mall. The owners agreed to split the cause equally. When 5 went out of business, the rest had to pay an addition 10 per month each. How many were in the original group?
Answer by SwiftAlbatross(13) (Show Source): You can put this solution on YOUR website!
Let x = the number of original business owners
$1000 / x = the amount each business owner paid
When 5 business owners were lost, there were x - 5 left and they had to pay what the 5 business owners would not. The 5 business owners paid
5 * ($1000 / x)
so we now pay this with $10 each from the remaining business owners
5 * ($1000 / x) = $10 * (x - 5)
Doing some algebra, we get
5 * 1000 / x = 10 (x - 5)
5000 = 10 * x * (x - 5)
500 = x^2 - 5x
x^2 - 5x - 500 = 0
(x - 25) * (x + 20) = 0
x = 25 OR x = -20
x can only be positive so x must be 25.
Checking the answer, we get 25 original business owners paying $1000 / 25, or $40 each. When 5 fold, there are 20 left and they have to pay the difference. Five business owners would have paid 5 * $40 which equals $200. The 20 remaining business owners pay $10 each so $10 * 20 equals to $200, so this is correct.
Therefore, there were 25 business owners in the original group.
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