В бюджете пончиковой компании Антона и Ксюши запланировано к концу второго года добиться снижения расходов по сравнению с текущими годовыми расходами на 19%. На сколько процентов нужно в течение этих двух лет снижать ежегодные расходы?

*a) Solution:* Let $x$ be the percentage by which expenses should be reduced each year. Then, after two years, the expenses will be $(1 - x/100)^2$ of the initial expenses. We want this to be equal to $1 - 0.19 = 0.81$ of the initial expenses. Thus, we have the equation: $$(1 - x/100)^2 = 0.81$$ Taking the square root of both sides, we get: $$1 - x/100 = 0.9$$ $$x/100 = 0.1$$ $$x = 10$$ Thus, the annual expenses should be reduced by 10%. *b) Solution:* Let $N$ be the number of employees two years ago. Then, after two years, the number of employees will be $N \cdot (1 + 0.20)^2$. We know that the current number of employees is 432. So, we have the equation: $$N Imes (1.2)^2 = 432$$ $$N Imes 1.44 = 432$$ $$N = \frac{432}{1.44} = 300$$ Thus, two years ago, the company had 300 employees. *Translation:* a) The annual expenses should be reduced by 10%. b) Two years ago, the company had 300 employees.