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 ?
"Will paid 1/3 of the dinner bill."
means Micah and Sue paid (1-1/3)=2/3 of the bill.
If Micah and Sue paid in the ratio 2:5, that means Sue paid 5/(2+5)=5/7 of their portion.
$6÷5/7=$8.40 which is 2/3 of the cost of dinner.
Proceeding the same way,
8.40÷2/3=$12.60 is the total cost of the dinner.
Let's set up the problem step by step.
Step 1: Let's assume the total cost of the dinner is "x" dollars.
Step 2: Will paid 1/3 of the bill. So, Will's payment is (1/3) * x = x/3 dollars.
Step 3: Micah and Sue paid in the ratio of 2:5. Let's assume that Micah paid 2y dollars and Sue paid 5y dollars (where "y" is a common factor between the two amounts).
Step 4: According to the problem statement, Sue paid $6 more than Will. So, we can set up an equation based on this information:
5y = (x/3) + 6
Step 5: Now, we have two equations based on the information given:
x/3 + 6 = 5y
x = 2y
Step 6: We can solve these equations simultaneously to find the values of x and y.
From equation (2): x = 2y
Substituting this value in equation (1): (2y)/3 + 6 = 5y
Step 7: Solving for y:
(2y)/3 + 6 = 5y
Multiply both sides by 3 to eliminate the fraction: 2y + 18 = 15y
Rearranging the equation: 15y - 2y = 18
Combining like terms: 13y = 18
Dividing both sides by 13 to solve for y: y = 18/13
Step 8: Now, we can substitute the value of y back into the equation to find the value of x:
x = 2y = 2 * (18/13) = 36/13
Step 9: The dinner cost, x, is 36/13 dollars.
To find out how much the dinner cost, we need to follow a step-by-step approach:
Step 1: Set up the equations
Let's assume that the total cost of the dinner is "x" dollars.
According to the given information:
Will paid 1/3 of the bill, which would be (1/3)*x = x/3 dollars.
Micah and Sue paid in a ratio of 2:5, which means they paid a total of 2 + 5 = 7 parts.
So, Micah's payment would be (2/7) * x dollars, and Sue's payment would be (5/7) * x dollars.
Also, we know that Sue paid $6 more than Will, so we can set up an equation: Sue's payment = Will's payment + $6.
Step 2: Solve the equations
Sue's payment = Will's payment + $6
(5/7) * x = (x/3) + $6
To simplify the equation, we can multiply both sides by the least common multiple (LCM) of 7 and 3, which is 21:
21 * [(5/7) * x] = 21 * [(x/3) + $6]
15x = 7x + $126
Combine like terms:
15x - 7x = $126
8x = $126
Divide both sides by 8 to solve for x:
x = $126 / 8
x = $15.75
So, the dinner cost $15.75.