Question

Реши задачу, выделяя три этапа математического моделирования: «В первой деревне на 49 домов больше, чем во второй. Определи, сколько домов в каждой деревне, если в двух деревнях всего 891 дом(-ов, -а)». Ответ: во второй деревне домов в первой деревне домов​

Answer 1

Всё решение с условием и ответом изображены на фото.

Answer 2

Mathematical Modeling of the Problem

To solve the problem of determining the number of houses in each village, we can break down the mathematical modeling into three main steps:

1. Defining the Variables: - Let's denote the number of houses in the first village as x and the number of houses in the second village as y.

2. Formulating the Equations: - We are given two pieces of information: - The first village has 49 more houses than the second village. - The total number of houses in both villages is 891. - We can express these pieces of information as a system of equations: - x = y + 49 (Equation 1) - x + y = 891 (Equation 2)

3. Solving the Equations: - We can solve the system of equations (Equation 1 and Equation 2) to find the values of x and y.

Solution

Let's solve the system of equations to find the values of x and y.

From Equation 1, we have x = y + 49. We can substitute this value of x into Equation 2:

y + 49 + y = 891

Solving for y: 2y + 49 = 891 2y = 891 - 49 2y = 842 y = 842 / 2 y = 421

Now that we have the value of y, we can find the value of x using Equation 1: x = 421 + 49 x = 470

So, the number of houses in the first village is 470, and the number of houses in the second village is 421.

Therefore, in the second village, there are 421 houses, and in the first village, there are 470 houses.

This solution satisfies both the given conditions and provides the required information.

Note: The solution has been derived using the provided mathematical modeling approach and equations.