Question

если к некоторой сумме денег прибавить через год 1/8 её часть,а в следующий- 1/8 новой суммы,то первоначальная сумма за два года увеличиться на 850 руб.Найти первоначальную сумму денег​

Answer 1

Ответ: пусть х- изначальная сумма

Тогда 1/8х+х -получившаяся сумма за первый год, (1/8х+х)1/8- за второй год

1/8х+х +(1/8х+х)1/8 - получившаяся сумма за 2 года

По условию задачи сумма изменилась на 850

850+х -сколько за два года получилось

Составим уравнение и решим его:

1/8х+х+(1/8х+х)•1/8=850+х

1/8х+х+1/64х+1/8х=850+х

17/64х+х-х=850

17/64х=850

х=850:17/64

x=850•64/17

x=3200

Ответ: 3200 рублей

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given that if we add 1/8 of a certain sum of money to it after one year, and then add 1/8 of the new sum to it in the following year, the initial sum will increase by 850 rubles. We need to find the initial sum of money.

Solution

Let's assume the initial sum of money is x rubles.

After one year, we add 1/8 of the initial sum to it, which is x/8 rubles. So, the new sum after one year is x + x/8 rubles.

In the second year, we add 1/8 of the new sum to it, which is (x + x/8)/8 rubles. So, the final sum after two years is x + x/8 + (x + x/8)/8 rubles.

According to the problem, the final sum after two years is 850 rubles more than the initial sum. So, we can write the equation:

x + x/8 + (x + x/8)/8 = x + 850

To solve this equation, we can simplify it step by step:

1. Multiply both sides of the equation by 8 to eliminate the denominators: 8x + x + (x + x/8) = 8x + 6800

2. Simplify the equation: 8x + x + x + x/8 = 8x + 6800 10x + x/8 = 8x + 6800

3. Multiply both sides of the equation by 8 to eliminate the fraction: 80x + x = 64x + 54400

4. Simplify the equation: 81x = 64x + 54400

5. Subtract 64x from both sides of the equation: 17x = 54400

6. Divide both sides of the equation by 17 to solve for x: x = 54400 / 17

Now, we can calculate the value of x to find the initial sum of money.