Question

Lady Moore's age is a multiple of 8 and 12 Her age is one away from a multiple of 7 She is younger than 60 years old. How old is Lady Moore?

Answer 1

To determine Lady Moore's age, we need to consider the given information:

1. Lady Moore's age is a multiple of 8 and 12.

2. Her age is one away from a multiple of 7.

3. She is younger than 60 years old.

Let's break this down step by step:

1. Find the common multiple of 8 and 12. The least common multiple (LCM) of 8 and 12 is 24. So, Lady Moore's age is a multiple of 24.

2. Her age is one away from a multiple of 7. We can start by listing the multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, and so on. Since her age is one away from a multiple of 7, we can subtract 1 from each multiple: 6, 13, 20, 27, 34, 41, 48, 55, 62, 69. We can see that 27 is one away from a multiple of 7.

3. She is younger than 60 years old. Since her age is a multiple of 24, and one away from a multiple of 7, we can narrow down the possible ages by considering multiples of 24 that are less than 60. The multiples of 24 less than 60 are: 24 and 48.

Therefore, Lady Moore's age can be either 24 or 48 years old.

Answer 2

Lady Moore's age is determined by finding the least common multiple (LCM) of 8 and 12 that is also one away from a multiple of 7 and less than 60. The LCM is 24, and testing its multiples reveals that Lady Moore's age is 48.

Step-by-step explanation:

The question requires solving a problem using number theory and arithmetic reasoning. We know that Lady Moore's age is a multiple of both 8 and 12, and one away from a multiple of 7, while also being younger than 60 years old. To find Lady Moore's age, we first have to find a common multiple of 8 and 12 which is less than 60.

The least common multiple (LCM) of 8 and 12 is 24. Multiples of 24 below 60 are 24, 48, and 72, but since we know she is younger than 60, we exclude 72. So we have two possibilities for her age: 24 or 48.

Now we need to find which of these numbers is one away from a multiple of 7. Adding or subtracting one from each: 23 and 25 for the first case, and 47 and 49 for the second case. Here we see that 49 is indeed a multiple of 7, so Lady Moore's age must be 48, as it's one away from 49.