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?
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
To find out how much the dinner cost, we need to determine the individual amounts paid by each person and then add them up.
Let's start by assigning variables:
- Let "x" be the total cost of the dinner bill.
According to the given information:
- Will paid 1/3 of the dinner bill, which means he paid (1/3) * x.
- Micah and Sue's combined ratio is 2:5. So, we need to determine the ratio's values. Let's assume Micah's ratio is "2x" and Sue's ratio is "5x".
- Sue paid $6 more than Will, which means Sue paid (1/3) * x + $6.
Now we can create an equation to solve for "x":
(1/3) * x + (2x + 5x) = x + $6
Simplifying the equation:
(1/3) * x + 7x = x + $6
(1/3) * x + 7x - x = $6
(1/3) * x + 6x = $6
(10/3) * x = $6
Now we can solve for "x":
10x = 18
x = 18/10
x = $1.80
Therefore, the dinner cost $1.80.