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
Algebra.Com
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?
---------------
Let the # in the group be "x".
If each paid his/her share the cost would be 288/x per person.
-------------
But two did not pay for their share so "x-2" shared the cost.
The new share was 288/(x-2) per person.
--------------
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)
==============
Cheers,
Stan H.
RELATED QUESTIONS
a group of friends went out to dinner and had a bill that totaled $288. WHen it came time (answered by stanbon)
A large family went to a restaurant for a buffet dinner the price of the dinner was $12... (answered by ikleyn)
A group of friends go out to dinner one evening. They agree to share the R1 120 bill... (answered by jorel1380)
A group of friends planned a trip and chartered a bus for 300$. When 3 more friends... (answered by Stitch)
Three friends ate dinner at a restaurant. The friends decided to add a 15% tip and then... (answered by mananth)
Bill and a group of friends decided to rent a house in Aspen Colorado for a week of... (answered by ankor@dixie-net.com,mananth,josgarithmetic)
maria took a group of clients out to dinner, and the total bill was $227.68 including... (answered by Mathtut)
Maria took a group of clients out to dinner, and the bill was $227.68 including tax.If... (answered by nerdybill)
A group of students went to the pub after the football game on Saturday night. They all... (answered by richwmiller)