gradma is exactly four times as old as her grandson sheridan, and sheridan is exactly three times as old as his little borther avery. if the sum of all three person's ages in 96, how old is avery?

Answer 1

Let Avery's age be \( a \).

Then Sheridan's age, who is three times as old as Avery, is: \[ s = 3a \]

Grandma, who is four times as old as Sheridan, is: \[ g = 4s = 4(3a) = 12a \]

According to the problem, the sum of their ages is 96: \[ g + s + a = 96 \]

Substituting the expressions for \( g \) and \( s \): \[ 12a + 3a + a = 96 \] \[ 16a = 96 \]

Now, solving for \( a \): \[ a = \frac{96}{16} = 6 \]

So, Avery is \( \boxed{6} \) years old.

To verify, we can calculate the ages of Sheridan and Grandma:

• Sheridan's age: \[ s = 3a = 3 \times 6 = 18 \]
• Grandma's age: \[ g = 4s = 4 \times 18 = 72 \]

Calculating the sum of their ages: \[ g + s + a = 72 + 18 + 6 = 96 \]

This confirms our solution that Avery is indeed \( \boxed{6} \) years old.