Carole and Canter agree to share the cost of an $18.00 pizza based on how much each ate. If Carole ate 2/3 the amount Canter ate, how much should each pay?
Canter's share is x and x and Carol's share is 2x/3
x + 2x/3 = 5x/3 = 1
x = 3/5
Canter pays 3/5 of $18. Carol pays the rest.
To determine how much each should pay, we first need to find the ratio of how much Carole and Canter ate.
Let's assume Canter ate x amount of pizza.
According to the given information, Carole ate 2/3 of what Canter ate, which is (2/3) * x = 2x/3.
To find the total amount both ate, we add Carole's amount and Canter's amount:
x + 2x/3 = (3x + 2x)/3 = 5x/3
Since the total cost of the pizza is $18.00, we can set up a proportion to find how much each should pay based on the ratio of what they ate to the total amount:
Canter's share/Carole's share = x/(2x/3) = (3x/3) / (2x/3) = 3x/2x = 3/2
Now, let's determine the total shares:
Total shares = Canter's share + Carole's share = 3/2 + 1 = 5/2
To find how much each should pay, we divide the total cost by the total shares:
Total cost/Total shares = $18.00 / (5/2) = $18.00 * (2/5) = $7.20
Therefore, Carole should pay $7.20, and Canter should also pay $7.20.
To find out how much each should pay, we need to calculate the amount each person ate.
Let's assume that Canter ate x amount of the pizza. According to the question, Carole ate 2/3 the amount Canter ate, so Carole ate 2/3 * x.
Now, to find the total amount:
Canter's amount + Carole's amount = total amount
x + 2/3 * x = total amount
To make the calculation easier, let's get a common denominator for the fractions:
3/3 * x + 2/3 * x = total amount
(3x + 2x)/3 = total amount
5x/3 = total amount
Now, we know that the total amount is equal to the cost of the pizza, which is $18.00. So, we can set up the equation:
5x/3 = 18
To solve for x, we can isolate it by multiplying both sides of the equation by 3/5:
(5x/3) * (3/5) = 18 * (3/5)
x = 54/5
x = 10.8
Now that we know x, we can find how much each person should pay:
Canter's amount = x = 10.8
Carole's amount = 2/3 * x = 2/3 * 10.8 = 7.2
Therefore, Canter should pay $10.80, and Carole should pay $7.20 to share the cost of the pizza based on how much each ate.