A company has 2 mines: A and B. The production per person in mine A was 22,6 tons last year, and 27,9 tons in mine B. Last year 60% of the total production came from mine A. The question is the total production of the company per person.
I calculated: $0.6\cdot22.6+0.4\cdot27.9=27.72$. But according to the answer sheet this is not the right answer.
Indeed it is not correct. This reminds me of the following problem : A train runs at $200$kph for $300$km and then at $100$kph for $500$km. What's the average speed of the train?
You can't simply take the average. In your example you need to first calculate the population of each company. Denote them $x_A$ and $x_B$.
Total production from company $A$ is $22.6x_A$.
Total production from company $B$ is $27.9x_B$. Total production is $22.6x_A + 27.9x_B$.
Hence you have $$22.6x_A = 0.6(22.6x_A + 27.9x_B)\Longrightarrow x_B \approx 0.54x_A$$
If we make such that the total population is $1 = x_A + x_B$, then you have $x_A \approx 0.65$ and $x_B\approx 0.35$.
Hence the average production per person is : $$0.65\cdot 22.6 + 0.35\cdot 27.9 \approx 24.46$$