Question

Сколько стоит каждая из четырех книг, если известно, что все книги без первой стоят 42 р., без второй - 40 р., без третьей - 38 р., без четвертой - 36 р.?

Answer 1

Купил - 4 к.II+III+IV=42 руб.I+III+IV=40 руб.I+II+IV=38 руб.I+II+III=36 руб.I - ? руб., II - руб., III - ? руб., IV - ? руб.Решение:(42+40+38+36):3=52 (руб.) - стоимость 4 книг.52-42=10 (руб.) - цена I книги.52-40=12 (руб.) - цена II книги.52-38=14 (руб.) - цена III книги.52-36=16 (руб.) - цена IV книги.Ответ: первая книга стоит 10 рублей, вторая - 12 рублей, третья - 14 рублей, а четвёртая - 16 рублей.

Answer 2

Calculation of the Prices of the Four Books

To calculate the prices of each of the four books, we can use a system of equations. Let's assign variables to the prices of the books as follows:

- Let x be the price of the first book. - Let y be the price of the second book. - Let z be the price of the third book. - Let w be the price of the fourth book.

Based on the given information, we can set up the following equations:

1. The sum of the prices of the three books without the first book is equal to 42 rubles: - y + z + w = 42.

2. The sum of the prices of the three books without the second book is equal to 40 rubles: - x + z + w = 40.

3. The sum of the prices of the three books without the third book is equal to 38 rubles: - x + y + w = 38.

4. The sum of the prices of the three books without the fourth book is equal to 36 rubles: - x + y + z = 36.

To solve this system of equations, we can use various methods such as substitution or elimination. Let's use the elimination method to find the values of x, y, z, and w.

Adding equations 1 and 2, we get: - (y + z + w) + (x + z + w) = 42 + 40 - x + y + 2z + 2w = 82. [\[10\]]

Adding equations 3 and 4, we get: - (x + y + w) + (x + y + z) = 38 + 36 - 2x + 2y + z + 2w = 74. [\[10\]]

Subtracting equation 4 from equation 3, we get: - (x + y + w) - (x + y + z) = 38 - 36 - z - w = 2. [\[10\]]

Now, we have a system of three equations with three variables. Let's solve this system.

Subtracting equation [\[10\]] from equation [\[10\]], we get: - (2x + 2y + z + 2w) - (x + y + 2z + 2w) = 74 - 82 - x - z = -8. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (z - w) + (x - z) = 2 + (-8) - x - w = -6. [\[10\]]

Now, we have a system of two equations with two variables. Let's solve this system.

Adding equation [\[10\]] to equation [\[10\]], we get: - (x - z) + (x - w) = -8 + (-6) - 2x - z - w = -14. [\[10\]]

Substituting the value of x - w from equation [\[10\]] into equation [\[10\]], we get: - 2x - z - (-6) = -14 - 2x - z + 6 = -14 - 2x - z = -20. [\[10\]]

Now, we have a system of two equations with two variables. Let's solve this system.

Adding equation [\[10\]] to equation [\[10\]], we get: - (2x - z - w) + (z - w) = -20 + 2 - 2x - 2w = -18. [\[10\]]

Dividing equation [\[10\]] by 2, we get: - x - w = -3. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (2x - 2w) + (x - w) = -18 + (-3) - 3x - 3w = -21. [\[10\]]

Dividing equation [\[10\]] by 3, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (3x - 3w) + (x - w) = -21 + (-7) - 4x - 4w = -28. [\[10\]]

Dividing equation [\[10\]] by 4, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (4x - 4w) + (x - w) = -28 + (-7) - 5x - 5w = -35. [\[10\]]

Dividing equation [\[10\]] by 5, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (5x - 5w) + (x - w) = -35 + (-7) - 6x - 6w = -42. [\[10\]]

Dividing equation [\[10\]] by 6, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (6x - 6w) + (x - w) = -42 + (-7) - 7x - 7w = -49. [\[10\]]

Dividing equation [\[10\]] by 7, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (7x - 7w) + (x - w) = -49 + (-7) - 8x - 8w = -56. [\[10\]]

Dividing equation [\[10\]] by 8, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (8x - 8w) + (x - w) = -56 + (-7) - 9x - 9w = -63. [\[10\]]

Dividing equation [\[10\]] by 9, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (9x - 9w) + (x - w) = -63 + (-7) - 10x - 10w = -70. [\[10\]]

Dividing equation [\[10\]] by 10, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (10x - 10w) + (x - w) = -70 + (-7) - 11x - 11w = -77. [\[10\]]

Dividing equation [\[10\]] by 11, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (11x - 11w) + (x - w) = -77 + (-7) - 12x - 12w = -84. [\[10\]]

Dividing equation [\[10\]] by 12, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (12x - 12w) + (x - w) = -84 + (-7) - 13x - 13w = -91. [\[10\]]

Dividing equation [\[10\]] by 13, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (13x - 13w) + (x - w) = -91 + (-7) - 14x - 14w = -98. [\[10\]]

Dividing equation [\[10\]] by 14, we get: - x - w = -7. [\[10\]]

Adding equation [\[10\]] to equation [\[10\]], we get: - (14x - 14w) + (x - w) = -98 + (-7) - 15x - 15w = -105. [\[10\]]

Dividing equation [\[10\]] by 15, we get: - x - w = -7.