12) The price of the math Olympics mascot is given by the sum of the cost of raw materials and the cost of processing. Last year, the mascot cost 10 Euros. This year, the cost of raw materials has doubled, while the cost of processing has increased by 10%; as a result, this year the mascot costs 12 Euros. How much does the cost of raw materials affect the final price of the product this year?
(A) Less than 1 Euro
(D) between 3 and 4 Euros
(B) between 1 and 2 Euros
(C) between 2 and 3 Euros
12) The answer is (C)

Let $P$ and $L$ be the prices of raw materials and labor from last year, respectively. Taking into account the increases this year, the two prices are $2P$ and $11L / 10$, respectively. This gives us the system

$$
P+L=10, \quad 2P+11L / 10=12
$$

from which we find that $P=10 / 9$. To get the price of raw materials this year, we just need to multiply by 2, obtaining 20/9, which is between 2 and 3.