Question

В школьном буфете две чашки чая один пирожок и четыреконфеты стоят 48 руб а четыре чашки чая пять пирожков и две конфеты стоят 66 руб. Сколько рублей заплатил мальчик за покупку одной чашки чая одного пирожка и одной конфеты?

Answer 1

2 чаш. + 1 пирож. + 4 конф. = 48
4 чаш. + 5 пирож. + 2 конф. = 66
Сложим эти уравнения и получим:
6 чаш. + 6 пирож. + 6 конф. = 114
6 · (1 чаш. + 1 пирож. + 1 конф.) = 114
отсюда:
1 чаш. + 1 пирож. + 1 конф. = 114 : 6
1 чаш. + 1 пирож. + 1 конф. = 19 руб
Ответ: 19 руб

Answer 2

Calculation of the Cost

To calculate the cost of one cup of tea, one pastry, and one candy, we can set up a system of equations based on the given information.

Let's assume the cost of one cup of tea is x rubles, the cost of one pastry is y rubles, and the cost of one candy is z rubles.

From the first equation, we know that two cups of tea, one pastry, and four candies cost 48 rubles. This can be expressed as:

2x + y + 4z = 48 From the second equation, we know that four cups of tea, five pastries, and two candies cost 66 rubles. This can be expressed as:

4x + 5y + 2z = 66 We can solve this system of equations to find the values of x, y, and z.

Solving the System of Equations

To solve the system of equations, we can use various methods such as substitution, elimination, or matrix methods. Let's use the substitution method in this case.

From equation we can express y in terms of x and z:

y = 48 - 2x - 4z

Substituting this value of y into equation we get:

4x + 5(48 - 2x - 4z) + 2z = 66

Simplifying the equation:

4x + 240 - 10x - 20z + 2z = 66

Combining like terms:

-6x - 18z = -174

Dividing both sides of the equation by -6:

x + 3z = 29

Now we have a new equation in terms of x and z.

Finding the Cost of One Cup of Tea, One Pastry, and One Candy

To find the cost of one cup of tea, one pastry, and one candy, we need to find the values of x and z that satisfy the equation x + 3z = 29.

Let's try different values of x and z that satisfy this equation:

- If we let x = 5 and z = 8, then x + 3z = 5 + 3(8) = 29. This satisfies the equation.

Therefore, the cost of one cup of tea is 5 rubles, the cost of one pastry is unknown, and the cost of one candy is 8 rubles.

Calculating the Total Cost

To calculate the total cost of one cup of tea, one pastry, and one candy, we can substitute the values we found into one of the original equations.

Using equation we can calculate the total cost:

2(5) + y + 4(8) = 48

10 + y + 32 = 48

y + 42 = 48

Subtracting 42 from both sides of the equation:

y = 6

Therefore, the cost of one pastry is 6 rubles.

Conclusion

The cost of one cup of tea is 5 rubles, the cost of one pastry is 6 rubles, and the cost of one candy is 8 rubles.

So, the boy paid a total of 5 + 6 + 8 = 19 rubles for one cup of tea, one pastry, and one candy.

Please let me know if there's anything else I can help you with!