Question

Реши задачу составив уравнение. 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

12х+18у=840 общее количество листов

х+у=60 общее количество тетрадей

12(60-у)+18у=840

720-12у+18у=840

6у=840-720

6у=120

у=20 тетрадей по 18 листов

х=60 - 20= 40  тетрадей по 12 листов

Answer 2

Problem Analysis

We are given that 60 notebooks of two different types were made using 840 sheets of paper. Each notebook of one type requires 12 sheets, while each notebook of the other type requires 18 sheets. We need to find the number of notebooks of each type that were made.

Solution

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

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

1. The total number of notebooks: x + y = 60. 2. The total number of sheets of paper used: 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 have 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.

Combining like terms:

6y = 120.

Dividing both sides by 6:

y = 20.

Substituting this value of y back into equation 1, we get:

x + 20 = 60.

Simplifying the equation:

x = 40.

Answer

Therefore, the number of notebooks of the first type is 40, and the number of notebooks of the second type is 20.