SOLUTION: I have a problem (8th grade) that I can't get started on. "a group of friends eat at a restaurant and agreed to split the $6.00 bill equally. Two men left without paying and

Click here to see ALL problems on Linear-systems

Question 123287: I have a problem (8th grade) that I can't get started on. "a group of friends

eat at a restaurant and agreed to split the $6.00 bill equally. Two men left without paying and the remaining others were assessed .25 more. How many men in the party originally?"
It seems like a linear equation that has 2 variables. How much did each spend and how many men. I can't put it into equation form.
Found 4 solutions by Superownage, stanbon, scott8148, checkley71:
Answer by Superownage(7)   (Show Source):
You can put this solution on YOUR website!
okay, look
6.00/x(people) = y(payment per person)
If x-2= 50% increase on y, then there were 8 people because 8(100%)-2(25%) means there was a 25% increase on the tab, and 6.00/4= $1.00

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
"a group of friends eat at a restaurant and agreed to split the $6.00 bill equally. Two men left without paying and the remaining others were assessed .25 more. How many men in the party originally?"
It seems like a linear equation that has 2 variables. How much did each spend and how many men.
--------------------------
Assume there were originally "x" men.
Since the bill was $6 each man would have owed 6/x dollars
----------------------------
But two left so there were only "x-2" men.
The bill was still $6 so each would have to pay 6/(x-2) dollars
----------------------------
The latter payment was $0.25 more than the former:
EQUATION:
6/(x-2) - 6/x = 0.25
Divide thru b 6 to get:
1/(x-2) - 1/x = 0.0417
[x-(x-2)] = 0.0417x(x-2)
2 = 0.0417x(x-2)
x(x-2) = 48
x^2-2x-48=0
(x-8)(x+6)=0
Positive answer:
x = 8 (This the original number of men in the group)
===============
Cheers,
Stan H.

Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website!
let x="number of men"

(600/x)+25=600/(x-2)

multiplying by x(x-2) __ 600x-1200+25x^2-50x=600x __ 25x^2-50x-1200=0

x^2-2x-48=0 __ factoring __ (x-8)(x+6)=0

Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website!
6/X=[6/(X-2)]-.25
6/X=[6+.25X+.5]/(X-2)
6(X-2)=X(6-.25X+.5)
6X-12=6X-.25X^2+.5X
-.25X^2+.5X+12=0
.25X^2-.5X-12=0
(.25X-2)(X+6)=0
.25X-2=0
.25X=2
X=2/.25
X=8 ANSWER FOR THE NUMBER OF MEN BEFORE 2 LEFT.
PROOF
6/8=6/(8-2)-.25
.75=6/6-.25
.75=1-.25
.75=.75