While shopping, Edna noticed that three different pancake mixes indicated that they were the best value for the price. She also noticed that all three packages cost the same amount. She wanted to know how they could all be the best value if they all cost the same. So, she decided to do a comparison of the mixes.
Package A claims it makes 10 pancakes with a diameter of 6 inches.
Package B claims it makes 25 pancakes with a radius of 2 inches.
Package C claims it makes 50 pancakes with a circumference of 6.28 inches.
Based on the total pancake area, order the packages from most valuable to least valuable. Assume all three types of pancakes have the same thickness. Use 3.14 for .
To determine which pancake mix offers the best value, we need to calculate the total pancake area for each package.
Package A:
- Diameter = 6 inches
- Radius = 3 inches (half of the diameter)
- Area of one pancake = πr^2 = 3.14 * 3^2 = 28.26 square inches
- Total pancake area = 10 pancakes * 28.26 square inches = 282.6 square inches
Package B:
- Radius = 2 inches
- Area of one pancake = πr^2 = 3.14 * 2^2 = 12.56 square inches
- Total pancake area = 25 pancakes * 12.56 square inches = 314 square inches
Package C:
- Circumference = 6.28 inches
- Diameter = Circumference / π = 6.28 / π ≈ 2 inches
- Radius = 1 inch (half of the diameter)
- Area of one pancake = πr^2 = 3.14 * 1^2 = 3.14 square inches
- Total pancake area = 50 pancakes * 3.14 square inches = 157 square inches
Therefore, the packages can be ordered from most valuable to least valuable based on total pancake area as follows:
1. Package B (314 square inches)
2. Package A (282.6 square inches)
3. Package C (157 square inches)
So Package B would be the best value for the price, followed by Package A and then Package C.