Question

Решите задачу, выделяя три этапа математического моделирования: Цена персиков на 15 р. выше, чем цена абрикосов. Для консервирования компота купили 3 кг персиков и 7 кг абрикосов. По какой цене покупали фрукты, если вся покупка обошлась в 985 р.?

Answer 1

Х стоит кг абрикосов
х+15 стоит кг персиков
7х+3(х+15)=985
7х+3х+45=985
10х=940
х=94 рубля стоит кг абрикосов
94+15=109 рублей кг персиков

х стоит 1м³ в 2013 году
х-1 1м³в 2012 году
194х-203=191(х-1)
194х-203=191х-191
3х=12
х=4рубля стоит 1 м³ газа в 2013 году

Answer 2

Mathematical Modeling of Fruit Prices

To solve the problem of finding the prices of peaches and apricots, we can break it down into three stages of mathematical modeling:

Stage 1: Define the Variables - Let's denote the price of peaches as P and the price of apricots as A.

Stage 2: Formulate the Equations - We are given that the price of peaches is 15 rubles higher than the price of apricots. This can be expressed as: - P = A + 15.

- Additionally, the total cost of 3 kg of peaches and 7 kg of apricots is 985 rubles. This can be represented by the equation: - 3P + 7A = 985.

Stage 3: Solve the Equations - We can now solve the system of equations to find the prices of peaches and apricots.

Solution

- Using the given equations, we can solve for the prices of peaches and apricots. - From the equation P = A + 15, we can express A in terms of P: A = P - 15. - Substituting A = P - 15 into the equation 3P + 7A = 985 gives us: 3P + 7(P - 15) = 985. - Solving for P gives us the price of peaches.

Conclusion

- By following these three stages of mathematical modeling, we can determine the prices at which the peaches and apricots were purchased.