SOLUTION: A group of friends went to dinner and received a bill totaling $288. The group decided to treat two people whose birthdays were that month and split the charges equally among the r

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Question 129553: A group of friends went to dinner and received a bill totaling $288. The group decided to treat two people whose birthdays were that month and split the charges equally among the rest of the group. This resulted in each person having to pay $4.80 more than each would have paid had the bill been split equally among the entire group. How many people were in the dinner group?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A group of friends went to dinner and received a bill totaling $288. The group decided to treat two people whose birthdays were that month and split the charges equally among the rest of the group. This resulted in each person having to pay $4.80 more than each would have paid had the bill been split equally among the entire group. How many people were in the dinner group?
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Let the # in the group be "x".
If each paid his/her share the cost would be 288/x per person.
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But two did not pay for their share so "x-2" shared the cost.
The new share was 288/(x-2) per person.
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EQUATION:
New share - Old share = 4.80
288/(x-2) - 288/x = 4.80
Multiply thru by x(x-2) to get
288x - 288(x-2) = 4.8x(x-2)
576 = 4.8(x^2-2x)
x^2-2x-120 =0
(x-12)(x+10)=0
Positive answer:
x = 12 (original # of people in the group)
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Cheers,
Stan H.