Question

Відомо що 4кг огірків і 3кг помідорів коштували 34грн. Після того як огірки подорожчали на 50%, а помідори подешевшали на 20% за 2кг огірків і 5кг помідорів заплатили 36грн. знайдіть початкову вартість 1кг. огірків і 1кг помідорів.

Answer 1

Нехай початкова вартість 1 кг огірків - х грн, а 1 кг помідорів - у грн.
Тоді 4х + 3у = 34
А після змін 2*1,5х + 5*0,8у =36
Треба розвязати отриману систему рівнянь!


Відповідь: початкова вартість 1 кг огірків - 4 грн, 1 кг помідорів - 6 грн.

Answer 2

Calculation of the Initial Prices of Cucumbers and Tomatoes

To find the initial prices of cucumbers and tomatoes, we can set up a system of equations based on the given information.

Let's assume the initial price of 1 kg of cucumbers is x and the initial price of 1 kg of tomatoes is y.

From the given information, we know that 4 kg of cucumbers and 3 kg of tomatoes cost 34 UAH. This can be represented by the equation:

4x + 3y = 34 ---(Equation 1)

After the price increase of cucumbers by 50% and the price decrease of tomatoes by 20%, the cost of 2 kg of cucumbers and 5 kg of tomatoes is 36 UAH. This can be represented by the equation:

2(1.5x) + 5(0.8y) = 36 ---(Equation 2)

Now, let's solve this system of equations to find the initial prices of cucumbers and tomatoes.

Solving the System of Equations

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

Multiplying Equation 1 by 2 and Equation 2 by 4 to eliminate the coefficients of x, we get:

8x + 6y = 68 ---(Equation 3) 8x + 20y = 72 ---(Equation 4)

Subtracting Equation 3 from Equation 4, we get:

14y = 4

Dividing both sides by 14, we find:

y = 4/14 = 2/7

Substituting the value of y back into Equation 3, we can solve for x:

8x + 6(2/7) = 68 8x + 12/7 = 68 8x = 68 - 12/7 8x = 476/7 - 12/7 8x = 464/7 x = (464/7) / 8 x = 58/7

Therefore, the initial price of 1 kg of cucumbers is 58/7 UAH and the initial price of 1 kg of tomatoes is 2/7 UAH.

Please note that the above calculations are based on the given information and assumptions made.