Question

Решите задачу, составив систему уравнений.На 960 руб. можно купить 4 меча и 6 комплектов формы. Каковы цена мяча и одного комплекта, если на те же 960 руб. можно купить 2 мяча и 7 комплектов формы?Списабо!

Answer 1

{4x+6y=960

{2x+7y=960  *2

 

{4x+6y=960

{4x+14y= 1920

 

 

 

 

{960-6y=1920-14y

 

{8y=960

{y=120 

 

{x=60

Ответ    мяч стоит      60 руб  комплект    стоит  120р

 

Answer 2

Problem Analysis

We are given that with 960 rubles, we can buy 4 swords and 6 sets of uniforms. We are also given that with the same amount of money, we can buy 2 balls and 7 sets of uniforms. We need to find the price of one ball and one set of uniforms.

Let's assume the price of one ball is x rubles and the price of one set of uniforms is y rubles.

System of Equations

We can set up a system of equations based on the given information:

Equation 1: 4x + 6y = 960 (from the first scenario) Equation 2: 2x + 7y = 960 (from the second scenario)

Solving the System of Equations

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 x in terms of y: 4x = 960 - 6y x = (960 - 6y) / 4

Substituting this value of x into Equation 2: 2((960 - 6y) / 4) + 7y = 960

Simplifying the equation: (1920 - 12y + 28y) / 4 = 960 (1920 + 16y) / 4 = 960 1920 + 16y = 3840 16y = 3840 - 1920 16y = 1920 y = 1920 / 16 y = 120

Now, substituting the value of y back into Equation 1 to find x: 4x + 6(120) = 960 4x + 720 = 960 4x = 960 - 720 4x = 240 x = 240 / 4 x = 60

Solution

Therefore, the price of one ball is 60 rubles and the price of one set of uniforms is 120 rubles.

Please note that the search results provided did not contain relevant snippets to directly cite the solution. However, the solution is derived through a standard algebraic approach to solving a system of equations.