Average monthly salary

A total of 10 teachers work at one small school in Moravia. The monthly salary of each is 21,500 CZK or 21,800 CZK or 22,500 CZK according to their education and age. The average monthly salary for this school's teacher is 21 850 CZK. How many teachers of this school earn CZK 22 5000 per month?

Correct result:

c =  2

Solution:

$$\begin{gathered} a+b+c=10 \\ 21500a+21800b+22500c=10\cdot 21850 \\ 215a+218b+225c=2185 \\ 215(10-b-c)+218b+225c=2185 \\ a=10-5-2=3 \\ b=5 \\ c=2 \end{gathered}$$

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