Question 230895: Word Problem Six - A group of people come forward to claim a $1,000,000 lottery jackpot, which the winners are to share equally. Before the jackpot is divided, three more winning ticket holders show up. As a result, each person's share is reduced by $75,000. How many winners are there and what were their shares? (Show a complete algebraic solution for the problem and check the answer.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A group of people come forward to claim a $1,000,000 lottery jackpot, which the winners are to share equally. Before the jackpot is divided, three more winning ticket holders show up. As a result, each person's share is reduced by $75,000. How many winners are there and what were their shares?
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Let the original group size of winners be "x";
The original average prize would be 1,000,000/x dollars
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Number of winners after 3 more join is "x+3"
New average prize is 1,000,000/(x+3) dollars
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Equation:
Original - New = 75000
1,000,000/x - 1,000,000/(x+3) = 75000
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Divide through by 75000 to get:
13.333/x - 13.333/(x+3) = 1
Multiply thru by x(x+3)
(40/3)(x+3) - (40/3)x = x^2+3x
Multiply thru by 3:
40x + 120 - 40x = 3x^2+9x
3x^2 + 9x -120 = 0
x^2 + 3x - 40 = 0
Positive Solution:
x = [-3 + sqrt(9-4*-40)]/2
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x = [-3 + sqrt(169)]/2
x = [-3 + 13]/2
x = 5 (original number of winners)
x+3 = 8 (total number of winners)
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1,000,000/8 = $125,000 (amount each winner received)
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Cheers,
Stan H.
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