Question

Упростите 1,5 (0,2а – 0,4 b) – 1,2 (a – 0,5 b) Решите задачу Известно, что 1кг колбасы на 120 рублей дешевле сыра. Купили 0,5 кг колбасы и 1кг сыра. За всю покупку заплатили 360 рублей. Сколько стоят продукты?

Answer 1

1)3а-6b-1,2а+6b=1,8а

Answer 2

Simplifying the Expression

To simplify the expression 1.5(0.2a - 0.4 + b) - 1.2(a - 0.5 + b), we can distribute the coefficients and combine like terms. Let's break it down step by step:

1. Distribute the coefficient 1.5 to each term inside the parentheses: - 1.5 * 0.2a = 0.3a - 1.5 * (-0.4) = -0.6 - 1.5 * b = 1.5b

2. Distribute the coefficient -1.2 to each term inside the second set of parentheses: - -1.2 * a = -1.2a - -1.2 * (-0.5) = 0.6 - -1.2 * b = -1.2b

3. Combine like terms: - 0.3a - 0.6 + 1.5b - 1.2a + 0.6 - 1.2b

Now, let's simplify the expression further by combining like terms:

- (0.3a - 1.2a) + (-0.6 + 0.6) + (1.5b - 1.2b) - -0.9a + 0 + 0.3b - -0.9a + 0.3b

Therefore, the simplified expression is -0.9a + 0.3b.

Solving the Problem

Now let's move on to solving the problem about the cost of products.

We are given that 1 kg of sausage is 120 rubles cheaper than 1 kg of cheese. Let's represent the cost of 1 kg of cheese as x rubles. Therefore, the cost of 1 kg of sausage would be x - 120 rubles.

Next, we are told that 0.5 kg of sausage and 1 kg of cheese were purchased for a total of 360 rubles.

Let's calculate the cost of the purchased products:

- Cost of 0.5 kg of sausage: 0.5 * (x - 120) - Cost of 1 kg of cheese: 1 * x

The total cost of the purchase is given as 360 rubles:

- 0.5 * (x - 120) + 1 * x = 360

Now, let's solve this equation to find the value of x (the cost of 1 kg of cheese):

- 0.5x - 60 + x = 360 - 1.5x - 60 = 360 - 1.5x = 420 - x = 420 / 1.5 - x = 280

Therefore, the cost of 1 kg of cheese is 280 rubles.

To find the cost of 1 kg of sausage, we can substitute the value of x into the expression x - 120:

- 280 - 120 = 160

Therefore, the cost of 1 kg of sausage is 160 rubles.

In summary, the products cost 280 rubles per 1 kg of cheese and 160 rubles per 1 kg of sausage.