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 did the dinner cost?

Go step by step how to do this problem

Its 42

$42

To solve this problem, we can break it down into manageable steps.

Step 1: Let's assign variables to the unknowns in the problem.

Let the total dinner bill be represented by "D."
Let Sue's payment be represented by "S."
Let Will's payment be represented by "W."
Let Micah's payment be represented by "M."

Step 2: Write down the given information in equations.

We are told that Will paid 1/3 of the dinner bill. So we can write:

W = (1/3)D     [Equation 1]

We are also told that Micah and Sue paid in a 2:5 ratio. We can represent this as:

M : S = 2 : 5

Since Sue paid $6 more than Will, we can rewrite this as:

S = W + $6     [Equation 2]

Step 3: Simplify the Micah and Sue ratio.

Since Micah and Sue paid in a 2:5 ratio, we know that the payment values are in the same proportion. We can express this as:

M/S = 2/5

To simplify this ratio, we can introduce a common factor to both sides:

(2/x) / (5/x) = 2/5

This simplifies to:

2/5 = 2/5

Step 4: Use the simplified ratio to find the relationship between Micah's payment and Sue's payment.

Since the ratio is simplified to 2/5, we can express Micah's payment in relation to Sue's payment as:

M = (2/5)S     [Equation 3]

Step 5: Substitute the value of S from Equation 2 into Equation 3.

Substituting (W + $6) for S in Equation 3, we have:

M = (2/5)(W + $6)

Step 6: Express Micah's payment in terms of D.

Using the relationship in Step 1, we know that Will's payment is (1/3)D, so we can express Micah's payment in terms of D as:

M = (2/5)(1/3)D + (2/5)($6)

Step 7: Substitute the values of M and W into the equation.

We now have expressions for both M and W in terms of D, so we can rewrite Equation 7 as:

(2/5)(1/3)D + (2/5)($6) = (1/3)D

Step 8: Solve for D.

Next, we can simplify and solve the equation for D.

Multiply through by 15 (the least common multiple of 5, 3, and 5):

(2/5)(1/3)(15)D + (2/5)($6)(15) = (1/3)(15)D

2D + 6($6)(3) = 5D

2D + $36 = 5D

3D = $36

D = $12

So, the dinner cost $12.

w+m+s=dc

w=dc/3
s=w+6
m/2=s/5 or m=2s/5

dc/3 +2s/5+s=dc
but s=dc/3 +6
dc/3+2/5 (dc/3 +6)+dc/3 +6=dc
check all that, and solve for dc

Thank you so much!

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Will micah and sue went to dinner.will paid 1 / 3 of the dinner bill.micah and sue paid in the ratio of 2 : 5.if sue paid 6 $ more than will how much did the dinner cost.