Question

Покупатель потратил пятую часть своих денег и половину остального. После этого у него осталось 200 рублей. Сколько денег у него было в начале

Answer 1

X - всего денег1/5x - потратил (x-1/5x):2=0.4x - потратил 0.4x=200x=500 - всего Проверка:покупатель потратил пятую часть своих денег и половину остатка1)500-100=400 руб ост после 1/5 траты2)400*1/2=200 руб ост

Answer 2

Problem Analysis

The buyer spent one-fifth of their money and half of what was left. After this, they had 200 rubles remaining. We need to determine how much money they had initially.

Solution

Let's assume that the initial amount of money the buyer had is represented by the variable x.

According to the problem, the buyer spent one-fifth of their money, which is x/5. After this expense, they had 4x/5 left.

Then, the buyer spent half of what was left, which is (4x/5)/2 or 2x/5. After this expense, they had (4x/5) - (2x/5) = 2x/5 left.

According to the problem, the remaining amount is 200 rubles. So we can set up the equation:

2x/5 = 200

To find the value of x, we can solve this equation.

Calculation

Let's solve the equation:

2x/5 = 200

Multiplying both sides of the equation by 5 to eliminate the fraction:

2x = 1000

Dividing both sides of the equation by 2 to solve for x:

x = 500

Answer

The buyer had 500 rubles initially.

Explanation

The buyer spent one-fifth of their money, which is 100 rubles (500/5). After this expense, they had 400 rubles left.

Then, the buyer spent half of what was left, which is 200 rubles (400/2). After this expense, they had 200 rubles remaining.

Therefore, the initial amount of money the buyer had was 500 rubles.