Question

Карандаш в 6 раз дешевле альбома,а ручка в 2 раза дешевле альбома.Альбом стоит на 2 рубля больше ,чем ручками карандаш вместе.Сколько. стоит альбом?

Answer 1

Пусть х - стоимость альбома. Тогда х/6 - стоимость карандаша, х/2 - стоимость ручки.
Уравнение:
х/6 + х/2 +2 = х
х - х/6 - х/2 = 2
6х/6 - х/6 - 3х/6 = 2
6х/6 - 4х/6 = 2
2х/6 = 2
2х = 2•6
2х=12
х=12/2
х=6 рублей стоит альбом

Answer 2

Problem Analysis

We are given the following information: - A pencil is 6 times cheaper than an album. - A pen is 2 times cheaper than an album. - The album costs 2 rubles more than the combined cost of the pen and pencil.

We need to determine the cost of the album.

Solution

Let's assume the cost of the album is x rubles.

According to the given information: - The pencil costs 6 times less than the album, so its cost is x/6 rubles. - The pen costs 2 times less than the album, so its cost is x/2 rubles. - The album costs 2 rubles more than the combined cost of the pen and pencil, so we have the equation: x = (x/6) + (x/2) + 2.

To solve this equation, we can simplify it by multiplying through by 6 to eliminate the fractions: 6x = x + 3x + 12.

Simplifying further, we get: 6x = 4x + 12.

Subtracting 4x from both sides, we get: 2x = 12.

Dividing both sides by 2, we find: x = 6.

Therefore, the album costs 6 rubles.

Answer

The album costs 6 rubles.

Verification

Let's verify the solution by substituting the value of x into the equation: 6 = (6/6) + (6/2) + 2.

Simplifying the equation, we get: 6 = 1 + 3 + 2.

Adding the numbers on the right side, we find: 6 = 6.

The equation is true, which confirms that the album costs 6 rubles.