Question

Составь систему уравнений для решения задачи, приняв за x стоимость 1 кг апельсинов, а за y - стоимость 1 кг яблок (в рублях). За 5 кг апельсинов и 3 кг яблок заплатили 450 рублей. Сколько стоит 1 кг каждого вида фруктов, если 3 кг яблок на 30 рублей дороже, чем 3 кг апельсинов? Очень надо!

Answer 1

Ответ:5x+3y=450

3y-3x=30

X=52,5;y=62,5.

Объяснение:

Answer 2

Problem Analysis

To solve this problem, we need to find the cost per kilogram of oranges (x) and apples (y) given the following information: - The cost of 5 kilograms of oranges and 3 kilograms of apples is 450 rubles. - The cost of 3 kilograms of apples is 30 rubles more than the cost of 3 kilograms of oranges.

Let's set up a system of equations to solve for x and y.

System of Equations

Let's define the following variables: - x: Cost per kilogram of oranges (in rubles) - y: Cost per kilogram of apples (in rubles)

From the given information, we can set up the following equations:

Equation 1: 5x + 3y = 450 (The cost of 5 kilograms of oranges and 3 kilograms of apples is 450 rubles)

Equation 2: 3y = 3x + 30 (The cost of 3 kilograms of apples is 30 rubles more than the cost of 3 kilograms of oranges)

Now, let's solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 2, we can rewrite it as: y = x + 10 (dividing both sides by 3)

Substituting this value of y into Equation 1, we get:

5x + 3(x + 10) = 450

Simplifying the equation:

5x + 3x + 30 = 450

Combining like terms:

8x + 30 = 450

Subtracting 30 from both sides:

8x = 420

Dividing both sides by 8:

x = 52.5

Now, substituting the value of x back into Equation 2 to find y:

y = 52.5 + 10

y = 62.5

Solution

Therefore, the cost per kilogram of oranges (x) is 52.5 rubles and the cost per kilogram of apples (y) is 62.5 rubles.