Question

Тетя Маша и тетя Даша пошли в магазин «Рублик» за покупками. Тетя Маша купила 3 кг макарон и 2 кг гречки и заплатила за это 249 руб. Тетя Даша купила 5 кг макарон и 1 кг гречки и заплатила за свою покупку 282 руб. Сколько стоит килограмм макарон и килограмм гречки в магазине «Рублик»?​

Answer 1

х  р. - стоит 1 кг макарон

у  р. - стоит 1 кг гречки

.

.

3х+2у=249

5х+у=282

.

у=282-5х

3х+2*(282-5х)=249

.

у=282-5х

3х+564-10х=249

.

у=282-5х

7х=564-249

.

у=282-5х

7х=315

.

у=282-5х

х=45

.

х=45

у=282-5*45

.

х=45(р.) - стоит 1 кг макарон

у=24(р.) - стоит 1 кг гречки

Answer 2

Calculation of the Price per Kilogram

To calculate the price per kilogram of macaroni and buckwheat at the "Rublik" store, we need to divide the total price by the total weight of each item purchased.

Let's start with Aunt Masha's purchase: - Aunt Masha bought 3 kg of macaroni and 2 kg of buckwheat. - She paid a total of 249 rubles for her purchase.

To find the price per kilogram of macaroni, we divide the total price by the total weight of macaroni: - Price per kilogram of macaroni = Total price of macaroni / Total weight of macaroni - Price per kilogram of macaroni = 249 rubles / 3 kg

Similarly, to find the price per kilogram of buckwheat, we divide the total price by the total weight of buckwheat: - Price per kilogram of buckwheat = Total price of buckwheat / Total weight of buckwheat - Price per kilogram of buckwheat = 249 rubles / 2 kg

Now let's move on to Aunt Dasha's purchase: - Aunt Dasha bought 5 kg of macaroni and 1 kg of buckwheat. - She paid a total of 282 rubles for her purchase.

To find the price per kilogram of macaroni, we divide the total price by the total weight of macaroni: - Price per kilogram of macaroni = Total price of macaroni / Total weight of macaroni - Price per kilogram of macaroni = 282 rubles / 5 kg

Similarly, to find the price per kilogram of buckwheat, we divide the total price by the total weight of buckwheat: - Price per kilogram of buckwheat = Total price of buckwheat / Total weight of buckwheat - Price per kilogram of buckwheat = 282 rubles / 1 kg

Calculation Results

Based on the given information, the price per kilogram of macaroni and buckwheat at the "Rublik" store is as follows:

- Price per kilogram of macaroni: - Aunt Masha: 249 rubles / 3 kg = 83 rubles per kilogram - Aunt Dasha: 282 rubles / 5 kg = 56.4 rubles per kilogram - Price per kilogram of buckwheat: - Aunt Masha: 249 rubles / 2 kg = 124.5 rubles per kilogram - Aunt Dasha: 282 rubles / 1 kg = 282 rubles per kilogram Please note that these calculations are based on the provided information and may not reflect the current prices at the "Rublik" store.