Question

За два килограмма винограда и один килограмм груш заплатили всего 5 евро. Если количество винограда уменьшить в 4 раза, а количество груш увеличить на 200 грамм, то за покупку нужно будет заплатить 2 евро 58 центов. Найди стоимость 1 кг винограда и стоимость 1 кг груш.

Answer 1

2Х+1У=5
2Х/4+(1+0,2)У=2,58

отсюда У=5-2Х

 подставляя получим 2Х/4+1,2(5-2Х) =2,58
Х=13,68/7,6=1,8 - цена винограда
5-2*1,8=1,4 - цена груш 

Answer 2

Calculating the Cost of Grapes and Pears

To find the cost of 1 kg of grapes and the cost of 1 kg of pears, we can use the given information and set up a system of equations to solve for the individual prices.

Let's denote: - the cost of 1 kg of grapes as x euros, and - the cost of 1 kg of pears as y euros.

According to the given information: 1. For 2 kg of grapes and 1 kg of pears, the total cost is 5 euros. 2. If the quantity of grapes is reduced by 4 times and the quantity of pears is increased by 200 grams, the total cost becomes 2.58 euros.

We can express these statements as equations and solve for x and y.

Setting Up the Equations

1. Equation 1: 2x + y = 5 (total cost for 2 kg of grapes and 1 kg of pears) 2. Equation 2: (x / 4) + (y + 0.2) = 2.58 (total cost after quantity adjustments)

Solving the Equations

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

Equation 1: 2x + y = 5

Equation 2: (x / 4) + (y + 0.2) = 2.58

After solving the system of equations, we find: - x = 1.6 euros (cost of 1 kg of grapes) - y = 1.5 euros (cost of 1 kg of pears)

Therefore, the cost of 1 kg of grapes is 1.6 euros and the cost of 1 kg of pears is 1.5 euros.

The solution is based on the provided information and the calculations performed.