Question

Четыре клюшки и две ракетки стоят 1680 рублей, а четыре ракетки и две клюшки стоят 1820 рублей. Что и на сколько рублей дороже: клюшка или ракетка? ЗАПИШИ РЕШЕНИЕ и ответ.

Answer 1

Пусть 1 клюшка - х, а 1 ракетка - у. Составим и решим систему уравнений:
4х + 2у = 1680
4у + 2х = 1820

Сократим оба уравнения на 2:
2х + у = 840
2у + х = 910

Выразим из первого уравнения у и подставим его значение во второе уравнение:
у= 840 - 2х
2 * ( 840 - 2х) + х = 910

Решим второе уравнение:
2 * ( 840 - 2х) + х = 910
1680 - 4 х + х = 910
-3х = 910 - 1680
-3х = - 770
х = 770 : 3 
х = 256,67
Тогда у = 840 - 2х = 840 - 2 * 256,67 = 326,66

Проверяем:
4 * 256,67 + 2 * 326,66 =1026,68 + 653,32 = 1680
4 * 326,66 + 2 * 256,67 = 1306,64 + 513,34 = 1820

Соответственно, 1 клюшка стоит 256,67 рублей, а 1 ракетка стоит 326,66 рублей.

Значит Ракетка стоит на 70 дороже:
326,66 - 256,67 = 70 рублей.

Ответ: Ракетка дороже клюшки на 70 рублей.

Answer 2

Problem Analysis

We are given the prices of four hockey sticks and two rackets, as well as the prices of four rackets and two hockey sticks. We need to determine which item is more expensive and by how much.

Solution

Let's assume the price of one hockey stick is x rubles and the price of one racket is y rubles.

According to the given information, four hockey sticks and two rackets cost 1680 rubles, and four rackets and two hockey sticks cost 1820 rubles.

From this information, we can set up the following equations:

Equation 1: 4x + 2y = 1680 Equation 2: 4y + 2x = 1820

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

From Equation 1, we can express y in terms of x: y = (1680 - 4x) / 2

Substituting this value of y into Equation 2, we get: 4((1680 - 4x) / 2) + 2x = 1820

Simplifying the equation: (3360 - 8x) + 2x = 1820 3360 - 6x = 1820 -6x = 1820 - 3360 -6x = -1540 x = -1540 / -6 x = 256.67

Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y: 4(256.67) + 2y = 1680 1026.68 + 2y = 1680 2y = 1680 - 1026.68 2y = 653.32 y = 653.32 / 2 y = 326.66

Therefore, the price of one hockey stick is approximately 256.67 rubles, and the price of one racket is approximately 326.66 rubles.

To determine which item is more expensive, we compare the prices of the hockey stick and the racket. Since the racket is priced at 326.66 rubles and the hockey stick is priced at 256.67 rubles, we can conclude that the racket is 70.99 rubles more expensive than the hockey stick.

Answer

The racket is approximately 70.99 rubles more expensive than the hockey stick.