Question

Большая коробка конфет в 2 раза дороже маленькой. Хотят купить 3 большие и 2 маленькие коробки, но если купить 2 большие коробки и 3 маленькие, то покупка будет дешевле на 15 руб. Сколько стоит каждая коробка?

Answer 1

Маленькая коробка-х руб,большая коробка - 2х руб. 

Получим уравнение:

(3*2х+2х) – (2*2х+3х)=15;

(6х+2х) – (4х+3х)=15;

8х – 7х = 15

х=15 руб( маленькая)

2)2*15=30 руб(большая коробка)

Answer 2

Problem Analysis

We are given that a large box of candies is twice as expensive as a small box. The goal is to determine the cost of each box. We are also given two scenarios: buying 3 large boxes and 2 small boxes, and buying 2 large boxes and 3 small boxes. The second scenario is cheaper by 15 rubles. We need to calculate the cost of each box.

Solution

Let's assume the cost of a small box of candies is x rubles. Since the large box is twice as expensive, the cost of a large box would be 2x rubles.

According to the first scenario, buying 3 large boxes and 2 small boxes, the total cost would be: 3 * (cost of a large box) + 2 * (cost of a small box) = 3 * (2x) + 2 * x = 6x + 2x = 8x rubles.

According to the second scenario, buying 2 large boxes and 3 small boxes, the total cost would be: 2 * (cost of a large box) + 3 * (cost of a small box) = 2 * (2x) + 3 * x = 4x + 3x = 7x rubles.

We are given that the second scenario is cheaper by 15 rubles. So, we can set up the following equation: 8x - 7x = 15 rubles.

Simplifying the equation, we get: x = 15 rubles.

Therefore, the cost of a small box of candies is 15 rubles, and the cost of a large box is 2 * 15 = 30 rubles.

Answer

Each small box of candies costs 15 rubles, and each large box costs 30 rubles.