Question

Молоко одной коровы содержит 5% жира, по другой 3,5%. Смешав молоко обеих коров, получили 10л молока, жирность которого составляет 4%. Сколько для этого использовали литров молока от каждой коровы ???

Answer 1

Пусть использовали х литров первой коровы и у литров второй.
По условию
х+у=10
4% от 10 литров - это 0,4 л жира в молоке,
этот жир состоит из 0,05х л жира молока первой коровы и
0,035у л жира молока второй коровы
Решаем систему двух уравнений

$\left \{ {{x+y=10} \atop {0,05x+0,035y=0,4}} \right.$

Выражем у из первого уравнения
у=10-х
и подставляем во второе

0,05х+0,035·(10-х)=0,4
0,05х+0,35-0,035х=0,4
0,015х=0,05
х=10/3

y=10-(10/3)=20/3

Ответ. 10/3 литров молока первой коровы и 20/3 литров молока второй

Answer 2

Calculation of Milk from Each Cow

To determine how much milk was used from each cow, we can set up a system of equations based on the given information.

Let's assume that x liters of milk were used from the cow with 5% fat content, and y liters of milk were used from the cow with 3.5% fat content.

From the given information, we know the following: - The milk from the first cow contains 5% fat. - The milk from the second cow contains 3.5% fat. - The total amount of milk obtained from both cows is 10 liters. - The fat content of the resulting mixture is 4%.

Based on these facts, we can set up the following equations:

Equation 1: x + y = 10 (since the total amount of milk obtained is 10 liters) Equation 2: (0.05x + 0.035y) / 10 = 0.04 (since the fat content of the resulting mixture is 4%)

To solve this system of equations, we can use substitution or elimination method.

Let's use the substitution method:

From Equation 1, we can express x in terms of y: x = 10 - y

Substituting this value of x into Equation 2, we get: (0.05(10 - y) + 0.035y) / 10 = 0.04

Simplifying the equation: (0.5 - 0.05y + 0.035y) / 10 = 0.04 (0.5 - 0.015y) / 10 = 0.04 0.5 - 0.015y = 0.04 * 10 0.5 - 0.015y = 0.4 -0.015y = 0.4 - 0.5 -0.015y = -0.1 y = -0.1 / -0.015 y = 6.67

Since we cannot have a fraction of a liter of milk, we can round the value of y to the nearest whole number. Therefore, y = 7 liters.

Substituting this value of y back into Equation 1, we get: x + 7 = 10 x = 10 - 7 x = 3

Therefore, 3 liters of milk were used from the cow with 5% fat content, and 7 liters of milk were used from the cow with 3.5% fat content.

Answer: To obtain a mixture of 10 liters of milk with a fat content of 4%, 3 liters of milk were used from the cow with 5% fat content, and 7 liters of milk were used from the cow with 3.5% fat content.