Question

В буфете продали одинаковое количество чашек кофе и пирожных.Чашка кофе и пирожное вместе стоили 50 р.. За весь кофе выручили 300 р,а за все пирожные 700 р. Сколько стоила чашка кофе и сколько стоило пирожное

Answer 1

300+700=1000 выручка буфета
1000:50=20 чашек кофе и пирожных продано
300:20=15 руб стоит чашка кофе
700:20=35 руб стоит пирожное или 50-15=35

Answer 2

Problem Analysis

We are given that the same number of coffee cups and pastries were sold in a cafeteria. The total cost of a coffee cup and a pastry together is 50 rubles. The total revenue from all the coffee cups sold is 300 rubles, and the total revenue from all the pastries sold is 700 rubles. We need to determine the cost of a coffee cup and the cost of a pastry.

Solution

Let's assume that the cost of a coffee cup is x rubles and the cost of a pastry is y rubles.

From the given information, we can form the following equations:

1. The total revenue from all the coffee cups sold is 300 rubles: - Number of coffee cups sold * Cost of a coffee cup = Total revenue from coffee cups - Number of coffee cups sold * x = 300 rubles

2. The total revenue from all the pastries sold is 700 rubles: - Number of pastries sold * Cost of a pastry = Total revenue from pastries - Number of pastries sold * y = 700 rubles

3. The total cost of a coffee cup and a pastry together is 50 rubles: - Cost of a coffee cup + Cost of a pastry = 50 rubles - x + y = 50 rubles

Since we are given that the same number of coffee cups and pastries were sold, we can assume that the number of coffee cups sold is equal to the number of pastries sold.

Let's solve these equations to find the values of x and y.

Solution Steps

1. Substitute the value of the number of coffee cups sold in equation 1 with the number of pastries sold. 2. Solve the resulting equation to find the value of x. 3. Substitute the value of x in equation 3 to find the value of y.

Solution

Let's solve the equations step by step:

1. Substitute the value of the number of coffee cups sold in equation 1 with the number of pastries sold: - Number of pastries sold * x = 300 rubles

2. Solve the resulting equation to find the value of x: - Number of pastries sold = 300 / x

3. Substitute the value of x in equation 3: - x + y = 50 rubles

4. Solve the resulting equation to find the value of y: - y = 50 - x

Now, let's substitute the value of y in equation 2: - Number of pastries sold * (50 - x) = 700 rubles

We can solve this equation to find the value of x and then substitute it back to find the value of y.

Let's solve the equations to find the values of x and y.

Solution Calculation

Substituting the value of y in equation 2: - Number of pastries sold * (50 - x) = 700 rubles

Substituting the value of the number of pastries sold in equation 2 with the number of coffee cups sold: - Number of coffee cups sold * (50 - x) = 700 rubles

Since the number of coffee cups sold is equal to the number of pastries sold, we can write: - Number of coffee cups sold * (50 - x) = 700 rubles

Substituting the value of the number of coffee cups sold in equation 1 with the number of pastries sold: - (300 / x) * (50 - x) = 700 rubles

Simplifying the equation: - (300 * (50 - x)) / x = 700

Cross-multiplying: - 300 * (50 - x) = 700 * x

Expanding: - 15000 - 300x = 700x

Combining like terms: - 1000x = 15000

Dividing both sides by 1000: - x = 15

Now, substituting the value of x in equation 3: - 15 + y = 50

Simplifying: - y = 50 - 15 - y = 35

Therefore, the cost of a coffee cup is 15 rubles, and the cost of a pastry is 35 rubles.

Answer

The cost of a coffee cup is 15 rubles, and the cost of a pastry is 35 rubles.