Will, Mike and Sue went to dinner. Will paid 1/3rd of the dinner bill. Mike and Sue paid in the ratio 2:5. If Sue paid $6 more than Will, how much did the dinner cost?
Let the cost of the bill = C
Will paid (1/3)C
Mike and Sue together paid (2/3) C
Mike paid (2/7) (2/3)C
Sue paid (5/7)(2/3)C
And
What Mike paid + $6 = What Sue paid .....so....
(2/7) (2/3)C + 6 = (5/7)(2/3)C
(4/21)C + 6 = (10/21)C
(10/21)C - (4/21)C = 6
(6/21)C = 6
C = 6(21/6) = $ 21
Proof
Will paid (1/3)(21) =$7
Mike paid (2/7) (2/3) (21) = $4
Sue paid $10