Question

Некто пожелал купить имение, но оно стоило a рублями более, чем у него было денег. Если б его капитал увеличился в n раз, то он не только мог бы уплатить требуемую сумму, но у него еще осталось бы столько денег, сколько теперь недостает. Как велик его капитал? Дайте решение при a = 3000, n = 1.5

Answer 1

Пусть х-изначальный капитал
тогда стоимость имения равна х+3000
если бы капитал увеличился в 1,5 раза, что составило бы 1,5х, то его хватило бы на покупку имения (х+3000) и осталось бы столько денег сколько теперь недостает, т.е 3000
Составим уравнение
1,5х-(х+3000)=3000
1,5х-х-3000=3000
0,5х=6000
х=12000

Answer 2

Problem Analysis

A person wants to buy an estate, but the cost of the estate is more than the money they have. If their capital increases by a certain factor, they would not only be able to pay the required amount but also have some money left. We need to determine the size of their capital given that a = 3000 and n = 1.5.

Solution

Let's assume the person initially has x amount of money. The cost of the estate is a. According to the problem, the cost of the estate is more than the money they have, so we can write the equation as:

a > x

If their capital increases by a factor of n, their new capital would be n * x. According to the problem, they would be able to pay the required amount and still have some money left. So we can write the equation as:

a = n * x + (a - x)

Simplifying the equation, we get:

a = n * x + a - x 0 = n * x - x 0 = x * (n - 1)

Since x cannot be zero, we can divide both sides of the equation by (n - 1) to solve for x:

x = 0 / (n - 1) x = 0

Therefore, the person's capital is 0.

Answer

The person's capital is 0.