SOLUTION: a group of friends went out to dinner and had a bill that totaled $288. WHen it came time to split the total cost of the bill equally, each person who was left (2 people left early

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Question 231172: a group of friends went out to dinner and had a bill that totaled $288. WHen it came time to split the total cost of the bill equally, each person who was left (2 people left early) had to pay an extra $4.80 on top of their own part to cover the price of the two missing people. How many people were in the original dinner group?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a group of friends went out to dinner and had a bill that totaled $288. WHen it came time to split the total cost of the bill equally, each person who was left (2 people left early) had to pay an extra $4.80 on top of their own part to cover the price of the two missing people. How many people were in the original dinner group?
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Let the original number in the group be "x":
Original average cost was 288/x dollars
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After two left there were "x-2" in the grou:
New average cost was 288/(x-2) dollars
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Equation
New average - old average = 4.80 dollars
288/(x-2) - 288/x = 4.8
Divide thru by 4.8 to get:
60/(x-2) - 60/x = 1
60x - 60(x-2) = x(x-2)
120 = x^2-2x
x^2-2x-120 = 0
(x-12)(x+10) = 0
Positive solution:
x = 12 (original number in the group)
Cheers,
Stan H.