To determine Mrs. Perry's age, let's analyze the given information:
1. Mrs. Perry's age is a multiple of 8 and 12:
The least common multiple of 8 and 12 is 24. Therefore, Mrs. Perry's age is a multiple of 24.
2. Mrs. Perry's age is two away from a multiple of 10:
This means her age is either two less than a multiple of 10 or two more than a multiple of 10.
3. Mrs. Perry is younger than 60 years old:
This sets an upper limit for her age.
Considering these conditions, we can determine the possible ages for Mrs. Perry:
- If Mrs. Perry's age is two less than a multiple of 10, it could be 18, 28, 38, or 48.
- If Mrs. Perry's age is two more than a multiple of 10, it could be 22, 32, 42, or 52.
However, we know that her age is also a multiple of 24. Among the possible ages listed, the only multiple of 24 is 48.
Therefore, Mrs. Perry is 48 years old.