SOLUTION: Good day I need help with the following question : 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

Question 1169281: Good day I need help with the following question :
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, while B’s portion of the bill was $5 less than C’s portion of the bill. The ratio 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 totaled $35,
a + b = 35
while B’s portion of the bill was $5 less than C’s portion of the bill.
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 and b with (c-5)
.8c + (c-5) = 35
1.8c = 35 + 5
1.8c = 40
c = 40/1.8
c = $22.22
:
Determine the total bill amount.
add to a + b = 35
35 + 22.22 = $57.22 is the total bill

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

Use the given ratio A:C = 4:5 to define

4x = A's portion
5x = C's portion

Then, since A's portion plus B's portion is $35,

35-4x = B's portion

Also, B's portion is $5 less than C's:

5x-5 = B's portion

Set the two expressions for B's share equal to each other:

The total amount of the bill in dollars is

Since that does not represent a whole number, either in dollars or in cents, I suspect the statement of the problem is incorrect.

RELATED QUESTIONS
Good day may you please help me with the following question. Thank you in advance.... (answered by josgarithmetic,greenestamps)
Good day. May you please assist me in the following question: Three friends A, B and C (answered by greenestamps)
good day please may you assist me in the following three friends A, B and C dine out... (answered by mahikab)
good evening Three friends A, B and C dine out and decide to split the bill according (answered by Boreal)
Three friends A, B and C dine out and decide to split the the bill according to what they (answered by Theo)
three friends A, B and C dine out and decide to split the bill according to what they... (answered by ikleyn)
Three friends A, B and C dine out and decide to split the bill according to what they... (answered by math_tutor2020)
Thre friends A, B and C dine out and decide to split the bill according to what they... (answered by ankor@dixie-net.com,greenestamps)
Today, 7 friends went out for lunch. Their total bill was $50.47 , including tax... (answered by rfer)