Question

Your cousin Brent is 6 3/4 years younger than your other cousin Eva. Your other cousin Ari is 10 5/12 years older than Brent. What is the difference in Eva’s age and Ari’s age in years

Answer 1

The difference in age between Eva and Ari, given the relative ages to Brent, is 3 2/3 years after converting mixed numbers to improper fractions and finding a common denominator to subtract.

Step-by-step explanation:

Let's work through the math to find the difference in age between Eva and Ari. If Brent is 6 3/4 years younger than Eva, we can represent Eva's age as B + 6 3/4. Ari is 10 5/12 years older than Brent, so Ari's age is B + 10 5/12. To find the difference between Eva's and Ari's ages, we subtract Eva's age from Ari's age:

1. First, express 6 3/4 as an improper fraction: 6 3/4 = 27/4.
2. Next, express 10 5/12 as an improper fraction: 10 5/12 = 125/12.
3. Subtract Eva's age from Ari's age in fraction form: (B + 125/12) - (B + 27/4).
4. To subtract, we must have a common denominator. The least common multiple of 4 and 12 is 12.
5. Convert 27/4 to an equivalent fraction with a denominator of 12: 27/4 = 81/12.
6. Subtract the fractions: 125/12 - 81/12 = 44/12.
7. Simplify the result: 44/12 = 3 2/3.

The difference in age between Eva and Ari is 3 2/3 years.