Question

Помогите, пожалуйста, решить эту задачу с помощью линейного уравнения! В магазине канцтоваров на верхней полке находилось 100 тетрадей, а на нижней 75, когда на нижнюю полку положили на 25 тетрадей меньше, чем на верхнюю. На верхней полке стало в 1,5 раза больше тетрадей, чем на нижней. Сколько тетрадей положили на каждую полку?

Answer 1

(100+x)/(75+x-25)=1.5
(x+100)/(x+75-25)=1.5
(x+100)/(x+50)=1.5
x+100=1.5*(x+50)
x+100=1.5x+75
x-1.5x=75-100
-0.5x=-25
x=-25/(-0.5)
x=50 тетрадей на верхнюю
50-25=25 тетрадей на нижнюю

Answer 2

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Answer 3

Problem Analysis

To solve this problem using a linear equation, we need to determine the number of notebooks placed on each shelf. Let's assign variables to represent the number of notebooks on the upper shelf and the lower shelf. We'll call the number of notebooks on the upper shelf "x" and the number of notebooks on the lower shelf "y".

Formulating the Equations

We are given the following information: - Initially, there were 100 notebooks on the upper shelf and 75 notebooks on the lower shelf. - When 25 notebooks were moved from the upper shelf to the lower shelf, the number of notebooks on the lower shelf became 25 less than the number on the upper shelf. - After the movement, the number of notebooks on the upper shelf became 1.5 times the number on the lower shelf.

Based on this information, we can create the following equations:

Equation 1: x - 25 = y (25 notebooks were moved from the upper shelf to the lower shelf) Equation 2: x = 1.5y (the number of notebooks on the upper shelf is 1.5 times the number on the lower shelf)

Solving the Equations

To solve this system of equations, we can substitute the value of x from Equation 2 into Equation 1:

1.5y - 25 = y

Simplifying the equation:

0.5y = 25

Dividing both sides by 0.5:

y = 50

Now, we can substitute the value of y back into Equation 2 to find the value of x:

x = 1.5 * 50 = 75

Answer

Therefore, 75 notebooks were placed on the upper shelf and 50 notebooks were placed on the lower shelf.

Note: The solution to this problem is based on the given information and the assumption that no other notebooks were added or removed from the shelves during the process.