Question

За 2 кг конфет и 3 кг печенья заплатили 480 р.Сколько стоит 1 кг печенья,и 1 кг конфет,если 1,5кг конфет дешевле 4кг печенья на 15 р.?

Answer 1

Подробное решение можно посмотреть во вложенном файле

Answer 2

Problem Analysis

We are given the information that 2 kg of candy and 3 kg of cookies were purchased for a total of 480 rubles. We need to determine the cost per kilogram of candy and cookies, given that 1.5 kg of candy is 15 rubles cheaper than 4 kg of cookies.

Solution

Let's assume the cost per kilogram of candy is x rubles and the cost per kilogram of cookies is y rubles.

From the given information, we can form two equations:

Equation 1: 2x + 3y = 480 (since 2 kg of candy and 3 kg of cookies were purchased for a total of 480 rubles)

Equation 2: 1.5x = 4y - 15 (since 1.5 kg of candy is 15 rubles cheaper than 4 kg of cookies)

We can solve these equations simultaneously to find the values of x and y.

Solving the Equations

Let's solve the equations using the substitution method.

From Equation 2, we can rewrite it as: 1.5x - 4y = -15

Now, we can solve this system of equations using substitution.

From Equation 1, we can express x in terms of y: 2x = 480 - 3y x = (480 - 3y) / 2

Substituting this value of x into Equation 2: 1.5 * ((480 - 3y) / 2) - 4y = -15

Simplifying the equation: 720 - 4.5y - 8y = -30 -12.5y = -750 y = -750 / -12.5 y = 60

Substituting the value of y back into Equation 1 to find x: 2x = 480 - 3 * 60 2x = 480 - 180 2x = 300 x = 300 / 2 x = 150

Answer

Therefore, the cost per kilogram of cookies is 60 rubles and the cost per kilogram of candy is 150 rubles.