Question

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

Answer 1

2х + 3у = 480
1,5х + 15 = 4у
у = (1,5х + 15) :4
у = 0,375х + 3,75

2х + 3(0,375х + 3,75) = 480
2х + 1,125х + 11,25 = 480
3,125х = 480 - 11,25
3,125х = 468,75
х = 468,75 : 3,125
х = 150 руб. - стоит 1 кг конфет

2 * 150 + 3у = 480
300 + 3у = 480
3у = 480 - 300
3у = 180
у = 180 : 3
у = 60 руб. - стоит 1 кг печенья

Answer 2

Пусть х-стоимость кг конфет
         у-стоимость кг печенья
2*х+3*у=480
4у-1.5х=15
1)150-стоимость конфет
2)60-стоимость печенья

Answer 3

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 C rubles and the cost per kilogram of cookies is P rubles.

From the given information, we can form the following equations: 1. 2C + 3P = 480 (equation 1) - This equation represents the total cost of 2 kg of candy and 3 kg of cookies. 2. 1.5C = 4P - 15 (equation 2) - This equation represents the price difference between 1.5 kg of candy and 4 kg of cookies.

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

From equation 2, we can express C in terms of P: C = (4P - 15) / 1.5

Substituting this value of C in equation 1, we get: 2 * ((4P - 15) / 1.5) + 3P = 480

Simplifying the equation: (8P - 30) / 1.5 + 3P = 480 8P - 30 + 4.5P = 720 12.5P = 750 P = 60

Now, substituting the value of P back into equation 2, we can find the value of C: C = (4 * 60 - 15) / 1.5 C = 165 / 1.5 C = 110

Therefore, the cost per kilogram of candy is 110 rubles and the cost per kilogram of cookies is 60 rubles.

Answer

The cost per kilogram of candy is 110 rubles and the cost per kilogram of cookies is 60 rubles.