Greggory and his little brother

Let the Gregory's present age be $x$ . Then his brother's age is $\dfrac x2$ .

• Next year the sum of their ages $x + 1 + \dfrac x2 + 1 = \dfrac {3x}2 + 2 = \dfrac 7{16}g$ , where $g$ is their grandpa's present age.
• Then their grandpa's age $g = \dfrac {24x+32}7$
• Their father's age $f = \dfrac g2 = \dfrac {12x+16}7$
• Their mother's age $m = f+4 = \dfrac {12x+16}7 + 4$
• Since Gregory was born when his mother was 22, then $m=x+22$ .

Then we have

$\begin{aligned} \frac {12x+16}7 + 4 & = x + 22 \\ 12x + 16 + 28 & = 7x + 154 \\ 5x & = 110 \\ \implies x & = \boxed{22} \end{aligned}$