Question

Реши задачу алгебраическим способом. На изготовление 60 тетрадей двух видов пошло 840 листов бумаги. На каждую тетрадь одного вида требовалось 12 листов, а на тетрадь другого вида- 18 листов. Сколько изготовили тетрадей каждого вида?

Answer 1

Всего изготовили 60 тетрадей: х+у=60
Ушло на изготовление 840 страниц, причем на одного вида 12листов, а на другого 18
12х+18у=840

Из первого уравнения выразим у и подставим во второе
у=60-х

12х+18(60-х)=840
12х+1080-18х=840
1080-840=18х-12х
240=6х
х=40

у=60-40=20
Ответ: по 12 листов изготовили 40 тетрадей, а по 18 листов изготовили 20 тетрадей

Answer 2

Problem Analysis

We are given that 840 sheets of paper were used to make 60 notebooks of two different types. One type of notebook requires 12 sheets of paper, while the other type requires 18 sheets of paper. We need to determine how many notebooks of each type were made.

Solution

Let's assume that the number of notebooks of the first type is represented by x, and the number of notebooks of the second type is represented by y.

From the given information, we can set up the following equations:

1. The total number of notebooks: x + y = 602. The total number of sheets of paper: 12x + 18y = 840 We can solve this system of equations to find the values of x and y.

Solving the System of Equations

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

From equation 1, we can express x in terms of y: x = 60 - y

Substituting this value of x into equation 2, we get: 12(60 - y) + 18y = 840

Simplifying the equation: 720 - 12y + 18y = 840 6y = 120 y = 20

Substituting the value of y back into equation 1, we can find x: x = 60 - 20 x = 40

Answer

Therefore, 40 notebooks of the first type and 20 notebooks of the second type were made.

Conclusion

Using algebraic methods, we determined that 40 notebooks of one type and 20 notebooks of the other type were made using 840 sheets of paper.