Jewellery boxes

Suppose that initially the jewels in $P$ are worth $(a + b + 5000)$,

and those in $Q$ are worth $(c + d + e)$.

The average value in $P$ at the start is $\frac {a + b + 5000}3$

After the jewel has been moved it is $\frac{a + b}2$.

Therefore:

$$\frac{a+b+5000}{3}=\frac{a+b}{2}-1000$$

Multiplying by $6$ and collecting like terms gives $a + b = 16000$

The average value in $Q$ at the start is $\frac {c + d + e}3$

After the jewel has been moved, the average value is $\frac{c + d + e + 5000}4$

Therefore:

$$\frac{c+d+e}{3}=\frac{c+d+e+5000}{4}-1000$$

Multiplying by $12$ and collecting like terms gives $c + d + e = 3000$.

Therefore the total value is

$$a+b+5000+c+d+e=16000+5000+3000=24000$$