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

720 листов ушло бы если бы по 12
840- 720 = 120 листов для других тетрадей
120 \ ( 18 - 12 ) = 20  тетрадей по 18 листов
60 - 20 = 40 тетрадей по 12 листов

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 find out how many notebooks of each type 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.

According to the given information, the total number of sheets used for the first type of notebook is 12x, and for the second type of notebook is 18y. The total number of sheets used is 840.

So, we can write the following equation: 12x + 18y = 840

To find the values of x and y, we need to solve this equation.

Solving the Equation

To solve the equation, we can use various methods such as substitution, elimination, or graphing. Let's use the substitution method.

We can rearrange the equation to solve for x: 12x = 840 - 18y x = (840 - 18y) / 12

Now, we can substitute this value of x into the equation: 12((840 - 18y) / 12) + 18y = 840

Simplifying the equation: 840 - 18y + 18y = 840 840 = 840

The equation is true for any value of y. This means that there are infinitely many solutions to this problem. We can choose any value for y and find the corresponding value of x.

Let's choose a value for y and find the corresponding value of x.

If we choose y = 0, then x = (840 - 18(0)) / 12 = 840 / 12 = 70. So, if we make 70 notebooks of the first type and 0 notebooks of the second type, the total number of sheets used will be 12(70) + 18(0) = 840.

If we choose y = 10, then x = (840 - 18(10)) / 12 = 660 / 12 = 55. So, if we make 55 notebooks of the first type and 10 notebooks of the second type, the total number of sheets used will be 12(55) + 18(10) = 840.

Similarly, we can choose other values of y and find the corresponding values of x.

In conclusion, there are infinitely many solutions to this problem. We can make different combinations of notebooks of the first and second types as long as the total number of sheets used is 840.

Please let me know if I can help you with anything else.