Question

За 4 кг апельсинів і 6 кг лимонів заплатили 465грн. Скільки коштує 1 кг апельсинів і скільки коштує 1 кг лимонів, якщо 3 кг лимонів дешевші за 4 кг апельсинів на 15 грн?

Answer 1

To solve this problem, we can set up a system of equations based on the given information. Let's denote the cost of 1 kg of oranges as x and the cost of 1 kg of lemons as y.

From the given information, we know that: 4 kg of oranges + 6 kg of lemons = 465 UAH

This can be written as: 4x + 6y = 465

We also know that: 3 kg of lemons are cheaper than 4 kg of oranges by 15 UAH

This can be written as: 4x - 3y = 15

We now have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solving the System of Equations

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

Multiplying the second equation by 2, we get: 8x - 6y = 30

Now, we can subtract the second equation from the first equation: (4x + 6y) - (8x - 6y) = 465 - 30 10y = 435 y = 43.5

Substituting the value of y back into the second equation, we can solve for x: 4x - 3(43.5) = 15 4x - 130.5 = 15 4x = 145.5 x = 36.375

Answer

Therefore, 1 kg of oranges costs approximately 36.38 UAH and 1 kg of lemons costs approximately 43.50 UAH.

Please note that these values are approximate, as the given information does not provide exact prices for oranges and lemons.