document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #469412 by nerdybill(7384) $\"\"$ $\"About$

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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?
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\n" ); document.write( "Let x = original number in group
\n" ); document.write( "and y = original share
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\n" ); document.write( "xy = 2400 (equation 1)
\n" ); document.write( "(x-2)(y+100) = 2400 (equation 2)
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\n" ); document.write( "solve equation 1 for y:
\n" ); document.write( "xy = 2400
\n" ); document.write( "y = 2400/x
\n" ); document.write( "substitute above into equation 2 and solve for x:
\n" ); document.write( "(x-2)(y+100) = 2400
\n" ); document.write( "(x-2)(2400/x+100) = 2400
\n" ); document.write( "multiplying both sides by x:
\n" ); document.write( "(x-2)(2400+100x) = 2400x
\n" ); document.write( "dividing both sides by 100:
\n" ); document.write( "(x-2)(24+x) = 24x
\n" ); document.write( "24x+x^2-48-2x = 24x
\n" ); document.write( "x^2+22x-48 = 24x
\n" ); document.write( "x^2-2x-48 = 0
\n" ); document.write( "(x+6)(x-8) = 0
\n" ); document.write( "x = {-6, 8}
\n" ); document.write( "throw out the negative solution (extraneous) leaving
\n" ); document.write( "x = 8 (answer)
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