Final answer:
By setting up equations based on the given relationships between the three individuals' ages, we find that the greatest possible age for Abigail is 17 years old.
Step-by-step explanation:
Let's assign variables to represent the ages of Abigail (A), Brenda (B), and Carly (C). From the problem, we have the following relationships:
- Abigail is 5 years older than Brenda: A = B + 5
- Brenda is twice as old as Carly: B = 2C
- The total of their ages is less than 40: A + B + C < 40
Now we can use the information to express all ages in terms of Carly's age. Since B = 2C, we can substitute B in the first equation to get A in terms of C:
A = 2C + 5
Now let's substitute A and B in the third equation with the expressions involving C:
(2C + 5) + (2C) + C < 40
Combine like terms to get:
5C + 5 < 40
Subtract 5 from both sides:
5C < 35
Divide by 5:
C < 7
Since C must be a whole number less than 7 and B is twice C, the maximum C could be is 6. That would make B equal to 12 (since 2 * 6 = 12) and A would then be 17 (since 12 + 5 = 17). Since the sum of their ages should be less than 40, with C = 6, B = 12, and A = 17, their ages would add up to 35, which is acceptable.
Therefore, the greatest possible age for Abigail is 17 years old.