Question

6. Решите задачу, составив систему уравнений: За 3 кг мандаринов и 6 кг апельсинов заплатили 3600 тенге. Сколько стоит 1 кг каждого вида фруктов, если 3 кг апельсинов на 1000 тенге дешевле, чем 4 кг мандаринов? Срочно!!!!!! ДАЮ 50 БАЛЛОВ

Answer 1

Ответ:

Пошаговое объяснение:

Мандарины X тг/кг

Апельсины Y тг/кг

Из условия:

3x+6y=3600 тг

4x-3y=1000 тг

Выразим x из первого уравнения

3x=3600-6y и разделим его на 3

x=1200-2y

подставим найденный x во второе уравнение

4*(1200-2y)-3y=1000

4800 - 8y-3y=1000

4800-11y=1000

4800-1000=11y

3800=11y

y=3800/11

y≈345,45 (цена апельсинов)

x мы выражали выше: x=1200-2y

x=1200-(2*345,45)

x=1200-690,8

x=509,2 (цена мандаринов)

Проверяем:

3x+6y = 3*509,2+6*345,45=1527,6+2072,7=3600,3 ≈ 3600 тг

4x-3y = 4*509,2-3*345,45=2036,8-1036,35=1000,45 ≈1000 тг

Странно что ответ не целый а округленный, в таких задачах обычно ответ целыми числами выражен, но у меня получается так.

Answer 2

Problem Analysis

To solve this problem, we need to find the cost per kilogram for both mandarins and oranges. We are given that the total cost of 3 kg of mandarins and 6 kg of oranges is 3600 tenge. Additionally, we know that the cost of 3 kg of oranges is 1000 tenge less than the cost of 4 kg of mandarins.

Let's assign variables to represent the cost per kilogram of mandarins and oranges. We'll use x for the cost per kilogram of mandarins and y for the cost per kilogram of oranges.

System of Equations

We can set up a system of equations based on the given information:

Equation 1: Cost of 3 kg of mandarins + Cost of 6 kg of oranges = 3600 tenge Equation 2: Cost of 3 kg of oranges = Cost of 4 kg of mandarins - 1000 tenge

Let's solve this system of equations to find the values of x and y.

Solution

To solve the system of equations, we'll use the substitution method. We'll solve Equation 2 for the cost of 3 kg of oranges and substitute it into Equation 1.

Equation 2: Cost of 3 kg of oranges = Cost of 4 kg of mandarins - 1000 tenge Simplifying Equation 2, we get: 3y = 4x - 1000

Now, we'll substitute this expression for the cost of 3 kg of oranges into Equation 1:

Equation 1: Cost of 3 kg of mandarins + Cost of 6 kg of oranges = 3600 tenge Substituting the expression for the cost of 3 kg of oranges, we get: 3x + 6(4x - 1000) = 3600

Simplifying the equation: 3x + 24x - 6000 = 3600 27x - 6000 = 3600 27x = 9600 x = 9600 / 27 x ≈ 355.56

So, the cost per kilogram of mandarins is approximately 355.56 tenge.

To find the cost per kilogram of oranges, we'll substitute the value of x into Equation 2: 3y = 4(355.56) - 1000 3y = 1422.24 - 1000 3y = 422.24 y = 422.24 / 3 y ≈ 140.75

So, the cost per kilogram of oranges is approximately 140.75 tenge.

Answer

Therefore, the cost per kilogram of mandarins is approximately 355.56 tenge and the cost per kilogram of oranges is approximately 140.75 tenge.

Please note that the values are approximate due to rounding.