Will, Micah, and Sue went to dinner. Will paid 1/3 of the dinner bill. Micah and Sue paid in the ratio 2:5. If Sue paid $6 more than will, how much di the dinner cost?

3 answers

Micah : Sue =2 : 5 or 2x : 5x
Let Will's share by y
total bill = y + 7x

Sue - Will = 6
5x - y = 6 or y = 5x-6

Will = (1/3)(total)
y = (1/3)(y+7x)
3y = y + 7x
2y = 7x ---> y = 7x/2

in y = 5x-6
7x/2 = 5x-6
7x = 10x - 12
3x=12
x=4
then y = 5(4)-6 = 14

So the dinner cost y + 7x = 14+7(4) = $42

check: Will paid (1/3) of 42.00 = $14.00
Micah paid 2x = 8.00
Sue paid 5x = 20.00
did Sue pay $6 more than Will ? YES
is 8 : 20 = 2:5 ? YES
All is good!

2+5=7
1/3
Sue=2/7

$18.20