9. (8 points) Grandma Li keeps her chickens in two courtyards, East and West. It is known that there are 40 chickens in the East courtyard. Now, she sells $\frac{1}{4}$ of the chickens in the West courtyard to the store, and $\frac{1}{3}$ to the processing plant. When the remaining chickens are added together, their total is exactly equal to 50% of the original total number of chickens in both the East and West courtyards. The original total number of chickens in the East and West courtyards is. $\qquad$
【Solution】Solution: As can be seen from the analysis diagram, the West Courtyard took away: $\frac{1}{4}+\frac{1}{3}=\frac{7}{12}$,

The West Courtyard is left with: $1-\frac{7}{12}=\frac{5}{12}$,
The amount taken away is more than what is left by: $\frac{7}{12}-\frac{5}{12}=\frac{1}{6}$, the 40 chickens of the East Courtyard account for $\frac{1}{6}$ of the West Courtyard's,

Therefore, the number of chickens in the West Courtyard is: $40 \div \frac{1}{6}=40 \times 6=240$ (chickens), so the total number of chickens originally raised in the East and West Courtyards is: $240+40=280$ (chickens). The answer is: 280