Question

За 20 тетрадей и один дневник ученик заплатил 125 тг. Какова цена одной тетради и цена одного дневника по отдельности, если за одну тетрадь и один дневник ученик заплатил 30тг?

Answer 1

Системой решение
20х + y =125
x+y =30   Метод подстановки

Во втором уравнении выражаем у ч\з х 
у=30-х Подставляем в 1 ур.
20х+30-х=125
19х=95
х=5
у=30-5
у=25
Ответ(5;25)

Answer 2

Problem Analysis

The problem states that a student paid 125 tenge for 20 notebooks and one diary. The question is to find the individual prices of a notebook and a diary if the student paid 30 tenge for one notebook and one diary.

Solution

Let's assume the price of one notebook is x tenge and the price of one diary is y tenge.

According to the given information: - The student paid 125 tenge for 20 notebooks and one diary. - The student paid 30 tenge for one notebook and one diary.

From the first statement, we can form the equation: 20x + y = 125 ---(1)

From the second statement, we can form the equation: x + y = 30 ---(2)

We can solve these two equations simultaneously to find the values of x and y.

Solving the Equations

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

From equation (2), we can express y in terms of x: y = 30 - x

Substituting this value of y in equation (1), we get: 20x + (30 - x) = 125

Simplifying the equation: 20x + 30 - x = 125 19x + 30 = 125 19x = 125 - 30 19x = 95 x = 95 / 19 x = 5

Now, substituting the value of x in equation (2), we can find the value of y: 5 + y = 30 y = 30 - 5 y = 25

Answer

The price of one notebook is 5 tenge and the price of one diary is 25 tenge.

Verification

To verify our answer, let's substitute the values of x and y in the given equations and check if they hold true.

From equation (1): 20x + y = 125 20(5) + 25 = 125 100 + 25 = 125 125 = 125 (True)

From equation (2): x + y = 30 5 + 25 = 30 30 = 30 (True)

Since both equations hold true, our answer is verified.

Conclusion

The price of one notebook is 5 tenge and the price of one diary is 25 tenge.