SOLUTION: A group of fishermen rented a boat for $2400. Two of the men withdrew from the party and as result, the share of each of those remaining was increased by 100. How many were in the

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Question 770277: A group of fishermen rented a boat for $2400. Two of the men withdrew from the party and as result, the share of each of those remaining was increased by 100. How many were in the original group?
Answer by nerdybill(7384) About Me  (Show Source):
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A group of fishermen rented a boat for $2400. Two of the men withdrew from the party and as result, the share of each of those remaining was increased by 100. How many were in the original group?
.
Let x = original number in group
and y = original share
.
xy = 2400 (equation 1)
(x-2)(y+100) = 2400 (equation 2)
.
solve equation 1 for y:
xy = 2400
y = 2400/x
substitute above into equation 2 and solve for x:
(x-2)(y+100) = 2400
(x-2)(2400/x+100) = 2400
multiplying both sides by x:
(x-2)(2400+100x) = 2400x
dividing both sides by 100:
(x-2)(24+x) = 24x
24x+x^2-48-2x = 24x
x^2+22x-48 = 24x
x^2-2x-48 = 0
(x+6)(x-8) = 0
x = {-6, 8}
throw out the negative solution (extraneous) leaving
x = 8 (answer)