Question 1170974: 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 protion of the bil totalled $35, while B's portion 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?
Answer by math_tutor2020(3817)   (Show Source):
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A = friend A's portion
B = friend B's portion
C = friend C's portion
A,B,C are positive real numbers and are values in dollars.
"A's portion and B's protion of the bil totalled $35"
So,
A+B = 35
"B's portion was $5 less than C's portion"
means that
B = C - 5
Go back to the first equation. Plug in B = C-5. Isolate C.
A+B = 35
A+C-5 = 35
A+C = 35+5
A+C = 40
C = 40-A
The ratio of A to C is 4:5, which means,
A/C = 4/5
5A = 4C .... cross multiply
5A = 4(40-A) .... plug in C = 40-A
5A = 160-4A
5A+4A = 160
9A = 160
A = 160/9
A = 17.7777777777778 .... which is approximate
A = 17.78 .... rounding to two decimal places
With this value of A, we can then find:
C = 40-A
C = 40-17.78
C = 22.22
And,
B = C - 5
B = 22.22 - 5
B = 17.22
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In summary, we found:
A's portion = $17.78
B's portion = $17.22
C's portion = $22.22
This means,
Total Bill = A+B+C = 17.78+17.22+22.22 = 57.22 dollars
Answer:
Total Bill = $57.22
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