Question

Aня и Таня весят вместе 40 кг.Таня и маня весят 50 кг.маня и Ваня весят 90 кг . ваня и даня весят 100кг . даня и аня весят 60 кг . СКОЛЬКО ВЕСЯТ ВСЕ ПО ОТДЕЛЬНОСТИ

Answer 1

Первое условие
х-вес ани
у- вес тани
х+у=40
второе условие
а-вес мани
а+у=50
Третье условие 
к-вес вани
а+к=90
Четвертое условие
п-вес дани
к+п=100
Пятое условие
х+п=60
уравнения
х+у=40
а+у=50
а+к=90
к+п=100
х+п=60
Так как вес каждого ребенка один,то в разных уравнениях он будет так же один. Тогда
складываем все уравнения и получаем
2а+2у+2х+2к+2п=340
а+у+х+к+п=170
вычтем из данного уравнения уравнение
а+у=50
и
к+п=100
и получим
тогда
а+у+х+к+п=170
а+у=50
х+к+п=120
к+п=100
х=20 --вес ани
тогда 
1)х+у=40
20+у=40
у=40-20
у=20 ---вес тани
2)а+у=50
а+20=50
а=50-20
а=30
а-вес мани
3)а+к=90
30+к=90
к=90-30
к=60
к-вес вани
4)к+п=100
60+п=100
п=100-60
п=40
п-вес дани
ПРОВЕРКА
1)таня+аня =40
20+20=40
2)таня+маня=50
20+30=50
3)маня+ваня=90
30+60=90
4)ваня+даня=100
60+40=100
5)даня+аня=60
40+20=60
Ответ ---- (аня-20 кг,таня-20 кг,маня-30 кг,ваня-60 кг,даня-40 кг)

Answer 2

Problem Analysis

We are given the weights of different pairs of people and we need to find the individual weights of each person.

Solution

Let's assign variables to each person's weight: - Ania's weight: A - Tanya's weight: T - Manya's weight: M - Vanya's weight: V - Danya's weight: D

We are given the following information: 1. Ania and Tanya together weigh 40 kg. 2. Tanya and Manya together weigh 50 kg. 3. Manya and Vanya together weigh 90 kg. 4. Vanya and Danya together weigh 100 kg. 5. Danya and Ania together weigh 60 kg.

We can set up a system of equations to represent this information:

Equation 1: A + T = 40 Equation 2: T + M = 50 Equation 3: M + V = 90 Equation 4: V + D = 100 Equation 5: D + A = 60

We can solve this system of equations to find the individual weights.

Solution Steps

1. Solve Equation 5 for D in terms of A: D = 60 - A 2. Substitute D in Equation 4: V + (60 - A) = 100 Simplify: V - A = 40 3. Solve Equation 3 for M in terms of V: M = 90 - V 4. Substitute M in Equation 2: T + (90 - V) = 50 Simplify: T - V = -40 5. Solve Equation 1 for T in terms of A: T = 40 - A 6. Substitute T in Equation 2: (40 - A) - V = -40 Simplify: -A - V = -80 7. Add Equation 6 and Equation 2: (-A - V) + (T - V) = -80 + (-40) Simplify: -A - V + T - V = -120 Combine like terms: -A + T - 2V = -120 8. Substitute T in Equation 7: -A + (40 - A) - 2V = -120 Simplify: -2A - 2V = -80 9. Divide Equation 8 by -2: A + V = 40 10. Add Equation 9 and Equation 6: (A + V) + (-A - V) = 40 + (-80) Simplify: 0 = -40

The equation 0 = -40 is not possible, which means there is no solution to this system of equations. It seems there is a contradiction in the given information.

Therefore, it is not possible to determine the individual weights of each person based on the given information.

Note: The given information may contain errors or inconsistencies.