Beer Bill
A group of friends stopped by the local pub for some beers. They decided to put charges on one bill. After a short time, two of the friends had to leave in a hurry and didn't leave their portion of the bill. The Total of the bill was $63. One of them said "Everyone throw in two dollars extra and we will have the bill covered exactly."
How many people were originally in the group ?
How many people were originally in the group ?
posted by Rajesh Lal at
11:24 PM
12 Comments:
9 people
7 dollars per person
9 people x 7 dollars = 63 dollar tab
two people leave, leaving 7 people
2 dollars per person x 7 remaining people covers the 14 dollar tab not paid by the 2 who left
Let x be the number of people originally
Let y be the portion each person needed to pay
the total bill will be
63=xy
two people left so we got
x-2
and everyone had to pay $2 more
y+2
therefore
63=(x-2)(y+2)
from the first equation we get
y=63/x
substitute it in the other formula and solve for x
63=(x-2)(63/x+2)
63=63+2x-126/x-4
0=2x-126/x-4
0=2x²-4x-126
0=2(x²-2x-63)
0=2(x-9)(x+7)
x=9, x=-7
we can't have negative amount of people so we are left with
x=9 people
9 people were origanlly there but 2 left so that in the end there was 7.
Assuming everyone had the same number of beers, there were 9 people. It seems odd, but the cost of the beer or the number of beers each is not relatived.
999,999,999. Then the beer bar fell.
the end
There were 9 cheap bastards who didn't tip their bartender.
Another way to solve is:
some number minus 2 (x - 2) is equal to the bill divided by the original number (63 / x). This gives us:
x - 2 = 63 / x
To get everything to one side we end up with:
x^2 - 2x - 63 = 0
Reverse FOIL (can't remember technical name lol) gives you:
(x+7)(x-9) = 0
So, there are now 7 people who have to pay $9 each. If there are 7 now, that means there were 9 making them each pay $7 each. So to sum up:
9 original people - 2 people gives 7 people.
7 people pay their bill of $7 (49) plus they each pay $2 (14) to cover the cheapscates bringing the total to 63!
~Calvin
And donkies just know that E=(mc)(mc)
i dont know why you guys come up with many different ways. I have a good one.
Ok p- people
m-money
P.m= 63
(P-2).(m+2)=63
ok what are 2 natural numbers that their product is 63 : 1.63 3.21 7.9.
Just by look at them and calculate in your mind. bingo. 7 and 9
2 people left, that means there were 9 people in the bar
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there was only 3 people
yes i was there
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