Question

Можно ли разменять купюру достоинством 1000 руб. купюрами достоинством 10 руб и 50 руб, если для размена можно использовать 26 купюр. надо решить через пусть и системой уровнения. помогите пожалуйста

Answer 1

Пусть х количество десятирублевых. У- количество пятидесятирублевых купюр. По условию составляем систему : х+у=26 и 10х+50у=1000 (эти два уравнения друг под другом с фигурной скобкой). Из первого: х=26-у Подставляем его в последнее: 10(26-у)+50у=1000 40у=740 у=18,5 но количество купюр может быть только целым числом, значит, такой размен невозможен.

Answer 2

Can I exchange a 1000 ruble banknote for 10 and 50 ruble banknotes using 26 banknotes?

To solve this problem, we can set up a system of equations. Let's assume that the number of 10 ruble banknotes is represented by x, and the number of 50 ruble banknotes is represented by y.

We are given the following information: - The total number of banknotes used for exchange is 26. - The value of the 10 ruble banknote is 10 rubles. - The value of the 50 ruble banknote is 50 rubles. - The value of the 1000 ruble banknote is 1000 rubles.

Based on this information, we can set up the following equations:

Equation 1: x + y = 26 (the total number of banknotes used for exchange is 26) Equation 2: 10x + 50y = 1000 (the total value of the banknotes used for exchange is 1000 rubles)

To solve this system of equations, we can use substitution or elimination. Let's use the elimination method:

Multiplying Equation 1 by 10, we get: 10x + 10y = 260

Subtracting Equation 2 from this new equation, we get: (10x + 10y) - (10x + 50y) = 260 - 1000 Simplifying, we have: -40y = -740 Dividing both sides by -40, we find: y = 18.5

Since we cannot have a fraction of a banknote, it means that the number of 50 ruble banknotes cannot be 18.5. Therefore, it is not possible to exchange a 1000 ruble banknote for 10 and 50 ruble banknotes using 26 banknotes.

Please let me know if there is anything else I can help you with!