Question

Шкала на весах начинается с 50 кг. Поэтому для определения своего веса ребята стали взвешиваться парами. Оказалось, что Коля и Толя вместе весят 57 кг, Коля и Олег - 54 кг, а Олег и Толя - 55 кг. Определите массу каждого мальчика

Answer 1

Т.к Коля+Толя=57 и Коля+Олег=54 то Толя тяжелее Олега на 3 кг 
по условию Олег+Толя=55
55-3=52 кг
52:2=26 весит Олег
26+3=29 весит Толя
54-26=28 весит Коля

Answer 2

Problem Analysis

The problem states that the scale on the weights starts at 50 kg. To determine their individual weights, the children started weighing themselves in pairs. The combined weight of Kolya and Tolya is 57 kg, Kolya and Oleg weigh 54 kg together, and Oleg and Tolya weigh 55 kg together. We need to determine the weight of each boy.

Solution

Let's assume that Kolya weighs x kg, Tolya weighs y kg, and Oleg weighs z kg. We can set up a system of equations based on the given information:

1. Kolya + Tolya = 57 kg 2. Kolya + Oleg = 54 kg 3. Oleg + Tolya = 55 kg

We can solve this system of equations to find the values of x, y, and z.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination. Let's use the elimination method:

From equations 1 and 2, we can subtract equation 2 from equation 1 to eliminate Kolya: (Kolya + Tolya) - (Kolya + Oleg) = 57 kg - 54 kg Tolya - Oleg = 3 kg -- Equation 4

From equations 2 and 3, we can subtract equation 3 from equation 2 to eliminate Oleg: (Kolya + Oleg) - (Oleg + Tolya) = 54 kg - 55 kg Kolya - Tolya = -1 kg -- Equation 5

Now we have a system of two equations: Tolya - Oleg = 3 kg -- Equation 4 Kolya - Tolya = -1 kg -- Equation 5

We can solve this system of equations to find the values of Tolya and Oleg.

Adding equation 4 and equation 5, we get: (Tolya - Oleg) + (Kolya - Tolya) = 3 kg + (-1 kg) Kolya - Oleg = 2 kg -- Equation 6

Now we have a new equation: Kolya - Oleg = 2 kg -- Equation 6

Adding equation 6 and equation 2, we get: (Kolya - Oleg) + (Kolya + Oleg) = 2 kg + 54 kg 2Kolya = 56 kg Kolya = 28 kg

Substituting the value of Kolya into equation 2, we get: 28 kg + Oleg = 54 kg Oleg = 54 kg - 28 kg Oleg = 26 kg

Substituting the values of Kolya and Oleg into equation 1, we get: 28 kg + Tolya = 57 kg Tolya = 57 kg - 28 kg Tolya = 29 kg

Answer

Based on the given information, Kolya weighs 28 kg, Tolya weighs 29 kg, and Oleg weighs 26 kg.

Kolya weighs 28 kg, Tolya weighs 29 kg, and Oleg weighs 26 kg.