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?
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Let x = original number in group
and y = original share
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xy = 2400 (equation 1)
(x-2)(y+100) = 2400 (equation 2)
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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)