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Abigail is 5 years older than Brenda.

Brenda is twice as old as Carly.

The total of their ages is less than 40.

What is Abigail’s greatest possible age?
Give your answer as a whole number of years.

Abigail is 5 years older than Brenda. Brenda is twice as old as Carly. The total of-example-1

1 Answer

7 votes

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.

User Rufus Pollock
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