Question

Купили 0,8 кг колбасы и 0,3 кг сыра. За всю покупку заплатили 25,56 р. Известно, что 1 кг колбасы дешевле 1 кг сыра на 4,9 р. Сколько стоит 1 кг сыра?

Answer 1

Пусть х руб. - цена 1 кг колбасы,тогда цена 1 кг сыра х+4,9
0,8х+0,3(х+4,9)=25,56
0,8х+0,3х+1,47=25,56
1,1х=24,09
х=21,9 руб. цена колбасы

21,9+4,9=26,8 руб. - цена сыра

Answer 2

Problem Analysis

To solve this problem, we need to find the cost of 1 kg of cheese. We are given the weights and prices of both sausage and cheese, as well as the total cost of the purchase. Additionally, we know that 1 kg of sausage is 4.9 rubles cheaper than 1 kg of cheese.

Solution

Let's break down the problem step by step:

1. Let's assume the cost of 1 kg of cheese is x rubles. 2. The cost of 1 kg of sausage will then be x + 4.9 rubles, as it is more expensive. 3. We can calculate the cost of 0.8 kg of sausage by multiplying the cost per kg by the weight: 0.8 * (x + 4.9) rubles. 4. Similarly, the cost of 0.3 kg of cheese will be: 0.3 * x rubles. 5. The total cost of the purchase is given as 25.56 rubles. 6. We can set up the equation: 0.8 * (x + 4.9) + 0.3 * x = 25.56. 7. Solving this equation will give us the value of x, which represents the cost of 1 kg of cheese.

Let's solve the equation:

0.8 * (x + 4.9) + 0.3 * x = 25.56

0.8x + 3.92 + 0.3x = 25.56

1.1x + 3.92 = 25.56

1.1x = 25.56 - 3.92

1.1x = 21.64

x = 21.64 / 1.1

x ≈ 19.67

Therefore, the cost of 1 kg of cheese is approximately 19.67 rubles.

Answer

The cost of 1 kg of cheese is approximately 19.67 rubles.