Question

Решите пожалуйста Купили 10 кг колбасы и 7 кг сыра. При этом оказалось, что 10 кг колбасы на 472 р. дороже 7 кг сыра, а 1 кг колбасы на 16 р. дороже 1 кг сыра. Определите стоимость покупки. Можно пожалуйста решение Ответ: 1928 р.

Answer 1

Problem Analysis

To solve this problem, we need to determine the cost of the purchase based on the given information. We are told that 10 kg of sausage is 472 rubles more expensive than 7 kg of cheese, and that 1 kg of sausage is 16 rubles more expensive than 1 kg of cheese.

Solution

Let's assume the cost of 1 kg of cheese is x rubles.

According to the given information, the cost of 10 kg of sausage is 472 rubles more than 7 kg of cheese. This can be expressed as:

10 kg of sausage = 7 kg of cheese + 472 rubles

Similarly, the cost of 1 kg of sausage is 16 rubles more than 1 kg of cheese:

1 kg of sausage = 1 kg of cheese + 16 rubles

To find the cost of the purchase, we need to calculate the total cost of 10 kg of sausage and 7 kg of cheese.

Let's solve the equations:

10 kg of sausage = 7 kg of cheese + 472 rubles 1 kg of sausage = 1 kg of cheese + 16 rubles

Multiplying the second equation by 10, we get:

10 kg of sausage = 10 kg of cheese + 160 rubles

Now we can substitute the value of 10 kg of sausage from the first equation into the second equation:

7 kg of cheese + 472 rubles = 10 kg of cheese + 160 rubles

Rearranging the equation, we get:

3 kg of cheese = 312 rubles

Now we can calculate the cost of 1 kg of cheese:

1 kg of cheese = 312 rubles / 3 kg = 104 rubles

To find the total cost of the purchase, we need to calculate the cost of 10 kg of sausage and 7 kg of cheese:

Cost of 10 kg of sausage = 10 kg * (1 kg of cheese + 16 rubles) = 10 kg * (104 rubles + 16 rubles) = 10 kg * 120 rubles = 1200 rubles

Cost of 7 kg of cheese = 7 kg * 104 rubles = 728 rubles

Total cost of the purchase = Cost of 10 kg of sausage + Cost of 7 kg of cheese = 1200 rubles + 728 rubles = 1928 rubles

Therefore, the cost of the purchase is 1928 rubles.

Conclusion

The cost of the purchase, consisting of 10 kg of sausage and 7 kg of cheese, is 1928 rubles.