Question

За четыре книги заплатили 132,5 р. Стоимость первой книги на 10% меньше стоимости второй, стоимость второй на 40% больше стоимости третьей, четвертая книга стоит на 16р больше третьей. Сколько стоит каждая книга? пж, очень нужно

Answer 1

Пусть 3-яя книга - 100%

140 от 3 книги - вторая

1 книга- 90 % от 2

4 книга - на 16 рублей больше чем 3-яя

Пусть 3 книга - x

0,9(1,4x) + x + (x+16) + 1.4x=132.5

4.66x+16=132.5

4,66x=132.5-16

x= 116.5/4.66

x=25

25р =  3-яя книга

1.4*25 = 35р - 2-я книга

0.9(35)= 31.5р - 1 книга

25 + 16 = 41р - 4 книга

Answer 2

Problem Analysis

We are given the following information: - The total cost of four books is 132.5 rubles. - The cost of the first book is 10% less than the cost of the second book. - The cost of the second book is 40% more than the cost of the third book. - The cost of the fourth book is 16 rubles more than the cost of the third book.

We need to find the cost of each book.

Solution

Let's assign variables to represent the costs of the books: - Let x be the cost of the first book. - Let y be the cost of the second book. - Let z be the cost of the third book. - Let w be the cost of the fourth book.

We can set up the following equations based on the given information: 1. x + y + z + w = 132.5 (equation 1) 2. x = 0.9y (equation 2) 3. y = 1.4z (equation 3) 4. w = z + 16 (equation 4)

We can solve this system of equations to find the values of x, y, z, and w.

Solving the Equations

Let's substitute equation 2 into equation 1 to eliminate x: 0.9y + y + z + w = 132.5 1.9y + z + w = 132.5 (equation 5)

Let's substitute equation 3 into equation 5 to eliminate y: 1.9(1.4z) + z + w = 132.5 2.66z + z + w = 132.5 3.66z + w = 132.5 (equation 6)

Let's substitute equation 4 into equation 6 to eliminate w: 3.66z + (z + 16) = 132.5 4.66z + 16 = 132.5 4.66z = 116.5 z = 116.5 / 4.66 z ≈ 25

Now, let's substitute the value of z back into equation 4 to find w: w = z + 16 w ≈ 25 + 16 w ≈ 41

Substituting the values of z and w into equation 3 to find y: y = 1.4z y ≈ 1.4 * 25 y ≈ 35

Finally, substituting the values of y, z, and w into equation 2 to find x: x = 0.9y x ≈ 0.9 * 35 x ≈ 31.5

Answer

Based on the calculations, we have found the following costs for each book: - The first book costs approximately 31.5 rubles. - The second book costs approximately 35 rubles. - The third book costs approximately 25 rubles. - The fourth book costs approximately 41 rubles.

Please note that the values are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.