Question

На 10 рублей в буфете можно купить 3 булочки- по 6 рулей и по 2 рубля. Сколько было куплено тех и других булочек? Нужно решить через уравнение.

Answer 1

Пусть булочки по 6 рублей будут обозначены х, а по 2 рубля у.
Составим систему уравнений 
{x+y=3
{6x+2y=10 из первого уравнения найдем х=3-у
6(х-у)+2у=10
Сократим на 2, получим 3(3-у)+у=5
9-3у+у=5
2у=4
у=2
значит булочек по 2 рубля было 2, а по 6 рублей одна

Answer 2

Problem Analysis

The problem states that with 10 rubles, you can buy 3 buns, with each bun costing 6 rubles and 2 rubles respectively. We need to determine how many of each type of bun was purchased. We can solve this problem using an equation.

Solution

Let's assume that the number of buns that cost 6 rubles is x, and the number of buns that cost 2 rubles is y. We can set up the following equation:

6x + 2y = 10

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

From the given information, we know that the total number of buns is 3. Therefore, we can write another equation:

x + y = 3

Now, we can solve this system of equations to find the values of x and y.

Solving the System of Equations

We can solve the system of equations using the substitution method. Let's solve the second equation for x:

x = 3 - y

Substituting this value of x into the first equation, we get:

6(3 - y) + 2y = 10

Simplifying the equation:

18 - 6y + 2y = 10

Combining like terms:

-4y = -8

Dividing both sides by -4:

y = 2

Now, substitute the value of y back into the second equation to find x:

x + 2 = 3

x = 1

Therefore, the number of buns that cost 6 rubles is 1, and the number of buns that cost 2 rubles is 2.

Answer

The number of buns that cost 6 rubles is 1, and the number of buns that cost 2 rubles is 2.