Question

4 блокнота и 3 ручки стоят 90 руб, а 3 блокнота дороже 2 ручек на 25 руб. Найдите цену блокнота и цену ручки( это решается в системе уравнения)

Answer 1

Пусть а коп - стоимость ручки, а б коп - стоимость блокнота. 
Тогда привдем условие задачи к системе уравнений 
4а+3б=90 
3а-2б=25. 
Воспользуемся методом алгебраического сложения, умножим каждое из уравнений на 2 и 3 соответственно. Получим систему вида: 
8а+6б=180 
9а-6б=75, 17а=255, а=15. 
Значит 15 копеек - стоимость блокнота. 
4*15+3б=90, 3б=30, б=10 
10 копеек - стоимость ручки

Answer 2

Problem Analysis

We are given the information that 4 notebooks and 3 pens cost 90 rubles, and that 3 notebooks are more expensive than 2 pens by 25 rubles. We need to find the price of a notebook and the price of a pen.

Solution

Let's assume the price of a notebook is x rubles and the price of a pen is y rubles.

From the given information, we can form the following equations:

Equation 1: 4x + 3y = 90 (since 4 notebooks and 3 pens cost 90 rubles) Equation 2: 3x - 2y = 25 (since 3 notebooks are more expensive than 2 pens by 25 rubles) To solve this system of equations, we can use the method of substitution or elimination.

Method of Substitution

We can solve Equation 2 for x and substitute it into Equation 1.

From Equation 2, we have: 3x - 2y = 25 3x = 25 + 2y x = (25 + 2y)/3

Substituting x into Equation 1, we get: 4((25 + 2y)/3) + 3y = 90 (100 + 8y)/3 + 3y = 90 100 + 8y + 9y = 270 17y = 170 y = 10

Substituting y = 10 into Equation 2, we can find x: 3x - 2(10) = 25 3x - 20 = 25 3x = 45 x = 15

Therefore, the price of a notebook is 15 rubles and the price of a pen is 10 rubles.

Conclusion

The price of a notebook is 15 rubles and the price of a pen is 10 rubles.