Prize Pony

Suppose that initially the ponies in the small stable are worth $(a + b + 250\ 000)$,
and those in the large stable are worth $(c + d + e)$.

The average value of the ponies in the small stable at the start is $\frac {a + b + 250\ 000}3$

After her favourite pony has been moved, the average value is $\frac{a + b}2$.

Since this increases the mean value of the ponies in the small stable by $10\ 000$:
\begin{equation}
\frac {a + b + 250\ 000}3 = \frac{a + b }{2} - 10\ 000
\end{equation}
Multiplying by $6$ and collecting like terms gives $a + b = 560\ 000$


The average value of the ponies in the large stable at the start is $\frac {c + d + e}3$

After her favourite pony has been moved, the average value is $\frac{c + d + e + 250\ 000}4$

Since this increases the mean value of the ponies in the large stable by $10\ 000$:
\begin{equation}
\frac {c + d + e}3 = \frac{c + d + e + 250\ 000}{4} - 10\ 000
\end{equation}
Multiplying by $12$ and collecting like terms gives $c + d + e = 630\ 000$.


Therefore the total value of the ponies is
$$a + b + 250\ 000 + c + d + e = 560\ 000 + 250\ 000 + 630\ 000 = 1\ 440\ 000$$