Question

За 7 кг апельсинов и 4 кг лимонов заплатили 26 Украинских гривней (гривен=100копеек).Сколько стоит 1 кг апельсинов и 1 кг лимонов если 5 кг апельсинов дороже 2 кг лимонов на 4 гривней????

Answer 1

$\left \{ {{7x+4y=26} \atop {5x=2y+4}} \right.$

14y+28+20y=130

28+34y=130

34y=102

17y=51

y=3

x=2

1 кг апельсинов стоит 2 гривны

1 кг лимонов стоит 3 гривны

 

Answer 2

To solve this problem, let's assign variables to the unknowns. Let's say the cost of 1 kg of oranges is x and the cost of 1 kg of lemons is y.

From the given information, we can create two equations:

Equation 1: 7x + 4y = 26 (equation representing the cost of 7 kg of oranges and 4 kg of lemons) Equation 2: 5x - 2y = 4 (equation representing the price difference between 5 kg of oranges and 2 kg of lemons)

To solve this 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: 5x = 4 + 2y x = (4 + 2y) / 5

Now, substitute this expression for x in Equation 1: 7((4 + 2y) / 5) + 4y = 26

Simplifying this equation will give us the value of y, which represents the cost of 1 kg of lemons.