SOLUTION: Thre friends A, B and C dine out and decide to split the bill according to what they order. A's portion and B's portion of the bill totalled $35, while B's portion of the bill was

Click here to see ALL problems on Equations

Question 1170897: Thre friends A, B and C dine out and decide to split the bill according to what they order. A's portion and B's portion of the bill totalled $35, while B's portion of the bill was $5 less than C's portion of the bill. The ration of A's portion to C's portion of the bill is 4:5. Determine the total bill amount.
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Three friends A, B and C dine out and decide to split the bill according to what they order.
A's portion and B's portion of the bill totalled $35,
a + b = 35
while B's portion of the bill was $5 less than C's portion of the bill.
b = c - 5
b - c = -5
The ratio of A's portion to C's portion of the bill is 4:5.
=
Cross multiply
5a = 4c
a = c
a = .8c
in the first equation, replace a with .8c, pair with the 2nd equation
b + .8c = 35
b - c = -5
------------Subtraction eliminates b, find c
0 + 1.8c = 40
c = 40/1.8
c = $22.22
then
a = .8(22.22)
a = $17.78
find b
17.78 + b = 35
b = 35 - 17.78
b = $17.22
Determine the total bill amount.
17.78 + 17.22 + 22.22 = $57.22

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Defective problem -- answers must be positive integers, but they are not.

A:C = 4:5, so
let 4x = A's portion
let 5x = C's portion
then 5x-5 = B's portion ($5 less than C's)

A's portion and B's portion together was $35:

Even if we go past the dollars to get cents, that does not provide a whole number answer.