A girl is three years older than her brother the product of their ages is 54 find their ages
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To find the ages of the girl and her brother, we can use a systematic approach by considering all possible pairs of ages whose product is 54. Here's how:
1. Start with the prime factorization of 54: 54 = 2 * 3 * 3 * 3.
2. Consider all possible ways to distribute these factors into two different ages, keeping in mind that the girl is three years older than her brother.
- Option 1: The brother's age is 2, and the girl's age is 27. (2 * 27 = 54)
- Option 2: The brother's age is 3, and the girl's age is 18. (3 * 18 = 54)
- Option 3: The brother's age is 6, and the girl's age is 9. (6 * 9 = 54)
Therefore, the possible ages are:
- Option 1: The girl is 27 years old, and her brother is 24 years old.
- Option 2: The girl is 18 years old, and her brother is 15 years old.
- Option 3: The girl is 9 years old, and her brother is 6 years old.