Question

За 5 кг яблок и 8 кг груш заплатили 35210 руб.Зная,что 7 кг груш дороже 3 кг яблок на 15690 руб.Найдите цену одного килограмма каждого фрукта. Помогите пожалуйста решить!))

Answer 1

Принимаем за х 1 кг яблок, а за у 1 кг груш;

Система:

{5x+8y=35210

{7y-3x=15690

 

5x=35210-8y

x=7042-1.6y

7y-3(7042-1.6y)=15690

7y-21126+4.8y=15690

11.8y=36816

y=3120 - цена 1 кг груш;

x=7042-1.6*3120=2050 - цена 1 кг яблок;

Ответ: 2050; 3130.

Answer 2

Problem Analysis

To solve this problem, we need to find the price per kilogram for both apples and pears. We are given the total cost of 5 kg of apples and 8 kg of pears, as well as the information that 7 kg of pears are more expensive than 3 kg of apples by 15,690 rubles.

Solution

Let's assume the price per kilogram of apples is x rubles and the price per kilogram of pears is y rubles.

From the given information, we can form two equations:

1. 5x + 8y = 35,210 (total cost of 5 kg of apples and 8 kg of pears) 2. 7y - 3x = 15,690 (7 kg of pears are more expensive than 3 kg of apples by 15,690 rubles)

We can solve this system of equations to find the values of x and y.

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

From equation 2, we can express x in terms of y: 3x = 7y - 15,690 x = (7y - 15,690) / 3

Substituting this value of x into equation 1, we get: 5((7y - 15,690) / 3) + 8y = 35,210

Simplifying the equation: 35y - 78,450 + 24y = 176,050 59y = 254,500 y = 4,310

Now, substituting the value of y back into equation 1, we can find the value of x: 5x + 8(4,310) = 35,210 5x + 34,480 = 35,210 5x = 730 x = 146

Therefore, the price per kilogram of apples is 146 rubles and the price per kilogram of pears is 4,310 rubles.

Answer

The price per kilogram of apples is 146 rubles and the price per kilogram of pears is 4,310 rubles.