Question

За 5 килограмм груш и 3 килограмм яблок, заплатили 72 гривны. Сколько стоит килограмм груш, если он дороже килограмма яблок на 8 гривен? (решите системой уравнений)​

Answer 1

Ответ:

Объяснение:

Пусть килограмм груш стоит х,а килограмм яблок у.

Тогда: 5х+3у=72,а х-у=8.

Решим систему

5х+3у=72

х-у=8

х=8+у

5*(8+у)+3у=72

40+5у+3у=72

8у=32

у=32:8

у=4 грн -килограмм яблок,

х=8+4  -килограмм груш.

х=12 грн-

Answer 2

Problem Analysis

We are given that 5 kilograms of pears and 3 kilograms of apples were purchased for a total of 72 hryvnias. We need to find the cost per kilogram of pears if they are more expensive than apples by 8 hryvnias per kilogram.

Solution

Let's assume the cost per kilogram of pears is x hryvnias. Since pears are more expensive than apples by 8 hryvnias per kilogram, the cost per kilogram of apples will be (x - 8) hryvnias.

According to the given information, the total cost of 5 kilograms of pears and 3 kilograms of apples is 72 hryvnias. We can set up the following equation:

5x + 3(x - 8) = 72

Now, let's solve this equation to find the value of x.

Solving the Equation

Expanding the equation, we get:

5x + 3x - 24 = 72

Combining like terms, we have:

8x - 24 = 72

Adding 24 to both sides of the equation, we get:

8x = 96

Dividing both sides of the equation by 8, we find:

x = 12

Answer

The cost per kilogram of pears is 12 hryvnias.

Verification

To verify our answer, let's substitute the value of x back into the equation:

5(12) + 3(12 - 8) = 72

Simplifying the equation, we have:

60 + 3(4) = 72

60 + 12 = 72

72 = 72

The equation is true, which confirms that our answer is correct.

Therefore, the cost per kilogram of pears is 12 hryvnias.