regular milk has 4% butterfat. How many litres of regular milk must be mixed with 40 L of milk with 1% butterfat to have milk with 2% butterfat?
To determine the quantity of regular milk needed, we can set up a mathematical equation based on the butterfat content.
Let "x" represent the amount of regular milk in liters that needs to be mixed.
The total amount of milk after mixing will be the sum of regular and low-fat milk, which is 40 L + x L.
Now, let's consider the butterfat content. The amount of butterfat in regular milk is 4% of x L, which is 0.04x liters of butterfat. The amount of butterfat in low-fat milk is 1% of 40 L, which is 0.01 * 40 = 0.4 liters of butterfat.
When we mix these two quantities, the total amount of butterfat will be the sum of the butterfat from regular and low-fat milk.
0.04x + 0.4 = 0.02 * (40 + x)
Now, let's solve this equation to find the value of x.
0.04x + 0.4 = 0.02 * 40 + 0.02x
0.04x + 0.4 = 0.8 + 0.02x
0.04x - 0.02x = 0.8 - 0.4
0.02x = 0.4
x = 0.4 / 0.02
x = 20
Therefore, 20 liters of regular milk must be mixed with the 40 liters of milk with 1% butterfat to obtain milk with 2% butterfat.
To solve this problem, we need to use the concept of a weighted average.
Let's first break down the given information:
- The regular milk has 4% butterfat.
- 40 liters of milk with 1% butterfat are given.
- We want to find out how many liters of regular milk need to be mixed with the given milk to obtain a mixture with 2% butterfat.
Let's assume that x liters of regular milk need to be mixed.
To find the solution, we can use the following formula for weighted average:
(Quantity 1 * Value 1) + (Quantity 2 * Value 2) = Total Quantity * Desired Value
In this case, we can set up the equation as follows:
(40 L * 1%) + (x L * 4%) = (40 L + x L) * 2%
Now let's solve for x:
(0.01 * 40) + (0.04 * x) = (40 + x) * 0.02
0.4 + 0.04x = 0.8 + 0.02x
0.04x - 0.02x = 0.8 - 0.4
0.02x = 0.4
x = 0.4 / 0.02
x = 20
Therefore, 20 liters of regular milk must be mixed with 40 liters of milk with 1% butterfat to obtain a mixture with 2% butterfat.
If x L are added, then
.01(40) + .04x = .02(40+x)
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