SOLUTION: Three friends A, B and C dine out and decide to split the 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

Question 1169511: Three friends A, B and C dine out and decide to split the 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.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A + B = 35
B = C - 5
A/C = 4/5

A + B = 35 and B = C - 5
replace B with C - 5 to get:
A + C - 5 = 35
add 5 to both sides of this equation to get:
A + C = 40
solve for A to get A = 40 - C

the ratio of A/C = 4/5 becomes (40 - C)/C = 4/5
cross multiply to get 4C = 5 * (40 - C)
simplify to get 4C = 200 - 5C
add 5C to both sides of this equation to get 9C = 200
solve for C to get C = 22.22

since A + B = 35, then A + B + C = 35 + 22.22 = 57.22

that's the total amount of the bill.
A and B paid 35
C paid 22.22.

B paid 5 less C, so B paid 17.22
that means A paid 17.78.

A paid 17.78
B paid 17.22
C paid 22.22

total for A and B was 35.

grand total was 57.22

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