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Question 1170803: good day please may you assist me in the following
three friends A, B and C dine out an decide to spilt 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.
Answer by mahikab(11)   (Show Source):
You can put this solution on YOUR website! Given:
(1) A:C = 4:5
=> A/C = 4/5
A = 4C/5
(2) A + B = $35
Substituting the value of A from (1) above,
4C/5 + B = 35
(4C/5 + B) * 5 = 35 * 5
4C + 5B = 175
(3) C - B = 5
5 * (C - B) = 5 * 5
5C - 5B = 25
Adding the equations from (2) and (3) above:
4C + 5B = 175
5C - 5B = 25
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9C = 200
C = 200/9 = $22.22
Substituting the value of C in the equation (3),
22.22 - B = 5
B = 22.22 - 5 = $17.22
Finally from equation (1),
A = 4C/5 = (4/5)*(200/9) = 160/9 = $17.77
Hence the solution:
A = $17.77
B = $17.22
C = $22.22
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