Question

в трех домах проживает 400 человек. две пятых числа жильцов первого дома равны одной третьей числа жильцов второго дома и две девятых третьего дома. Сколько человек проживает в каждом доме?

Answer 1

Обозначим х - число жильцов в первом доме, у - во втором доме и z - в третьем. Система уравнений с тремя неизвестными: x+y+z=400 (*) 2/5 x=1/3 y 2/5 x=2/9 z Выразим y и z через х. y=2/5*3*x=6/5x z=2/5*9/2*z=9/5x Подставляем в (*) x+6/5x+9/5x=400 (5/5+6/5+9/5)*x=400 4x=400 x=100 Подставляем в y и z. y=6/5x=6/5*100=600/5=120 z=9/5x=9/5*100=900/5=180 Ответ: в первом доме живет 100 человек, во втором - 120, в третьем - 180. надеюсь помогла)

Answer 2

Problem Analysis

We are given that there are 400 people living in three houses. The number of residents in the first house is equal to two-fifths of the number of residents in the second house, and the number of residents in the third house is equal to two-ninths of the number of residents in the second house. We need to determine the number of people living in each house.

Solution

Let's assume the number of residents in the second house is x.

According to the given information: - The number of residents in the first house is equal to two-fifths of x. - The number of residents in the third house is equal to two-ninths of x.

To find the number of residents in each house, we can set up the following equations:

1. Number of residents in the first house = (2/5) * x 2. Number of residents in the third house = (2/9) * x 3. Number of residents in the first house + Number of residents in the second house + Number of residents in the third house = 400

Let's solve these equations to find the values.

Calculation

1. Number of residents in the first house = (2/5) * x 2. Number of residents in the third house = (2/9) * x 3. Number of residents in the first house + Number of residents in the second house + Number of residents in the third house = 400

Substituting the values from equations 1 and 2 into equation 3, we get:

(2/5) * x + x + (2/9) * x = 400

Simplifying the equation:

(18/45) * x + (45/45) * x + (10/45) * x = 400

(73/45) * x = 400

Multiplying both sides by (45/73):

x = (400 * 45) / 73

x ≈ 246.575

Since the number of residents must be a whole number, we can round x to the nearest whole number:

x ≈ 247

Now, we can find the number of residents in each house:

- Number of residents in the first house = (2/5) * 247 ≈ 98 - Number of residents in the second house = 247 - Number of residents in the third house = (2/9) * 247 ≈ 54.889

Rounding the number of residents in the third house to the nearest whole number:

Number of residents in the third house ≈ 55

Answer

Therefore, there are approximately 98 people living in the first house, 247 people living in the second house, and 55 people living in the third house.