Question

Решите задачу,составляя уравнение. У Пети в 5 раз больше оловянных солдатиков,чем у Саши.Петя подарил Саше 8 своих солдатиков.После этого у него осталось в 3 раза больше солдатиков,чем стало у Саши.Сколько солдатиков было у каждого из мальчиков первоначально?

Answer 1

У Пети  5х оловянных солдатиков, у Саши - х. Петя подарил Саше 8 своих солдатиков и у него осталось 5х - 8. У Саши стало х + 8. После этого у него осталось в 3 раза больше солдатиков, чем стало у Саши. 5х - 8 = 3(х + 8) Сколько солдатиков было у каждого из мальчиков первоначально?
5х - 8 = 3(х + 8) = 3х + 24; 5х - 3х = 24 + 8: 2х = 32: х = 16 У Саши было 16 солдатиков. У Пети было 3х = 3х16 = 48 солдатиков.

Answer 2

Problem Analysis

Let's break down the problem step by step to solve it:

1. Petia has 5 times more tin soldiers than Sasha. 2. Petia gives 8 of his soldiers to Sasha. 3. After giving the soldiers, Petia has 3 times more soldiers than Sasha.

We need to find the initial number of soldiers for each boy.

Solution

Let's assume that Sasha initially had x tin soldiers. According to the problem, Petia had 5 times more soldiers than Sasha, so Petia initially had 5x tin soldiers.

After Petia gives 8 soldiers to Sasha, Petia has 3 times more soldiers than Sasha. This means that after the exchange, Petia has 3(x + 8) soldiers, and Sasha has x + 8 soldiers.

Now we can set up an equation to solve for x:

3(x + 8) = 5x

Let's solve this equation to find the value of x.

Solving the Equation

Expanding the equation:

3x + 24 = 5x

Subtracting 3x from both sides:

24 = 2x

Dividing both sides by 2:

x = 12

So, Sasha initially had 12 tin soldiers.

Now we can find the initial number of soldiers for Petia:

Petia = 5x = 5 * 12 = 60

Therefore, Petia initially had 60 tin soldiers.

Answer

The initial number of tin soldiers for each boy was: - Sasha: 12 - Petia: 60