Question

Помогите решить задачу! За 2кг яблок и 3кг слив заплатили 31 грн. За 3 кг яблок и 1 кг слив заплатили 29 грн. Найти стоимость 1 кг яблок и 1 кг слив. Заранее спасибо!

Answer 1

Пусть кг слив стоит х руб. Тогда 1 кг яблок стоит х+15 руб. Составим и решим уравнение: х+2(х+15)=180; х+2х+30=180; 3х=150; х=50. Значит, 1 кг слив стоит 50 руб, тогда 1 кг яблок стоит 50+15=65 руб. Ответ: 65 руб, 50 руб

Answer 2

Problem Analysis

To find the cost of 1 kg of apples and 1 kg of plums, we need to set up a system of equations based on the given information. Let's assume the cost of 1 kg of apples is A and the cost of 1 kg of plums is P.

From the first equation, we know that 2 kg of apples and 3 kg of plums cost 31 UAH: 2A + 3P = 31

From the second equation, we know that 3 kg of apples and 1 kg of plums cost 29 UAH: 3A + 1P = 29

We can solve this system of equations to find the values of A and P.

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.

Multiplying the first equation by 3 and the second equation by 2, we get: 6A + 9P = 93 6A + 2P = 58

Subtracting the second equation from the first equation, we eliminate A: (6A + 9P) - (6A + 2P) = 93 - 58 7P = 35 P = 5

Substituting the value of P back into the second equation, we can solve for A: 3A + 1(5) = 29 3A + 5 = 29 3A = 24 A = 8

Solution

The cost of 1 kg of apples is 8 UAH and the cost of 1 kg of plums is 5 UAH.

Please let me know if I can help you with anything else.