Final answer:
By setting up an equation based on the sum of the sisters' ages and testing the provided options, it is found that the oldest sister, Autumn, can be 22 years old as the sum of their ages would be 63, which is greater than their mother's age of 54.
Step-by-step explanation:
The question given involves finding the possible age of the oldest sister given the condition that the sum of the ages of three sisters is greater than 54, the age of their mother. Let's denote the ages of Autumn, Brittany, and Chloe by A, B, and C respectively. Based on the information that they are each one year apart, we can say B = A - 1 and C = B - 1 or C = A - 2.
Adding their ages together, we get the equation A + (A - 1) + (A - 2) > 54. Simplifying this gives us 3A - 3 > 54. Adding 3 to both sides, we get 3A > 57, and dividing both sides by 3, we find A > 19. To find the maximum possible age of the oldest sister, we need to consider options that are greater than 19, but the sum should not exceed the age of the mother.
If we test the given options:
- (a) A = 20: The total age would be 20 + 19 + 18 = 57, which is greater than 54. So, 20 is a possibility.
- (b) A = 21: The total age would be 21 + 20 + 19 = 60, which is greater than 54. So, 21 is also a possibility.
- (c) A = 22: The total age would be 22 + 21 + 20 = 63, which is still greater than 54. Therefore, 22 is a possibility and is also the largest option provided.
- (d) A = 23: Given this is not one of the options in the question, 22 remains the highest valid option.
Therefore, the correct answer is c) 22 years old.