Question

У двох мішках було по 60 кг борошна. Борошно з одного мішка розфасували в малі упаковки, а з іншого - у велики. Кожна мала упаковка містить борошна на 2 кг менше, ніж кожна велика, тому малих упаковок знадобилося на 8 більше, ніж великих. Скільки кілограмів борошна містить мала упаковка?

Answer 1

Объяснение:

Пусть малая упаковка муки содержит х кг.      ⇒

Большая упаковка муки содержит (х+2) кг.

$\frac{60}{x} -\frac{60}{x+2}=8\\ 60*(x+2)-60*x=8*x*(x+2)\\60x+120-60x=8x^2+16x\\8x^2+16x-120=0\ |:8\\x^2+2x-15=0\\D=64\ \ \ \ \sqrt{D}=8\\ x_1=-5\notin\ \ \ \ x_2=3\in.$

Ответ: малая упаковка муки содержит 3 килограмма.

Answer 2

Problem Analysis

To solve this problem, we need to determine the weight of flour in the small package. We know that there were two bags of flour, each containing 60 kg. The flour from one bag was packed into small packages, and the flour from the other bag was packed into large packages. Each small package contains 2 kg less flour than each large package, and the number of small packages needed was 8 more than the number of large packages.

Solution

Let's denote: - x as the weight of flour in the small package in kg. - y as the number of small packages. - z as the number of large packages.

We can create the following equations based on the given information: 1. x + 2 = (60 - x), as each small package contains 2 kg less flour than each large package. 2. y = z + 8, as the number of small packages needed was 8 more than the number of large packages. 3. x * y = (60 - x) * z, as the total weight of flour in the small packages equals the total weight of flour in the large packages.

Calculations

Let's solve the system of equations to find the value of x.

From equation 1: x + 2 = 60 - x 2x = 58 x = 29

Now, we can find the number of small packages: From equation 2: y = z + 8

And the number of large packages: z = y - 8

Substitute x = 29 into equation 3: 29y = 31z

Answer

The small package contains 29 kg of flour.