Twenty litres of milk with unknown butter-fat content from Vat A is mixed with 10 litres of milk with 3% butter-fat from Vat B to produce milk with 3 43 % butter-fat content. Find the percentage of butter-fat in Vat A.
make sure the fat content of the parts adds up to that of the mix.
20x + 10*.03 = 30*0.343
Now finish it off.
Well, isn't this a milky situation we've got here! So, let's break it down. We have 20 litres of milk from Vat A with an unknown butter-fat content, and 10 litres of milk from Vat B with 3% butter-fat. The final milk mixture has a butter-fat content of 3.43%.
To find the percentage of butter-fat in Vat A, we need to do a little math-sorcery. Let's assume that the percentage of butter-fat in Vat A is X%.
So, the total amount of butter-fat in the mixture can be calculated as follows:
(20 * X) + (10 * 3) = 30 * 3.43
Now, let's solve for X to unveil the butter-fat content in Vat A:
20X + 30 = 102.9
20X = 102.9 - 30
20X = 72.9
X = 72.9 / 20
Calculating... *Drumroll*...
The percentage of butter-fat in Vat A is approximately 3.65%.
Now, go butter up your day with this delightful result!
To find the percentage of butter-fat in Vat A, we can set up an equation based on the given information.
Let x be the percentage of butter-fat in Vat A.
According to the problem, there are 20 liters of milk from Vat A and 10 liters of milk from Vat B. The resulting mixture has a butter-fat content of 3.43%.
The total amount of milk in the mixture is 20 + 10 = 30 liters.
The amount of butter-fat in Vat A is 20 * (x/100) liters.
The amount of butter-fat in Vat B is 10 * (3/100) liters, since it has a butter-fat content of 3%.
The total amount of butter-fat in the mixture is (20 * (x/100)) + (10 * (3/100)) liters.
Since the resulting mixture has a butter-fat content of 3.43%, the total amount of butter-fat in the mixture is also 30 * (3.43/100) liters.
Setting up the equation:
(20 * (x/100)) + (10 * (3/100)) = 30 * (3.43/100)
Now, we can solve this equation to find the value of x, which represents the percentage of butter-fat in Vat A.
To find the percentage of butter-fat in Vat A, we need to set up an equation using the given information.
Let's denote the percentage of butter-fat in Vat A as x.
According to the given information:
- There are 20 litres of milk from Vat A with an unknown butter-fat content.
- There are 10 litres of milk from Vat B with 3% butter-fat content.
- The mixture of these two types of milk results in a final milk mixture with 3.43% butter-fat content.
To solve this problem, we can use the concept of the weighted average.
The weighted average can be calculated by multiplying the quantity of each item by its respective value, summing these values, and then dividing by the total quantity.
Let's calculate the weighted average for the butter-fat content in the mixture:
(20 liters * x%) + (10 liters * 3%) = (30 liters * 3.43%)
Now, we can simplify this equation:
(20x) + (0.3) = (102.9)
20x + 0.3 = 102.9
20x = 102.9 - 0.3
20x = 102.6
x = 102.6 / 20
x ≈ 5.13
Therefore, the percentage of butter-fat in Vat A is approximately 5.13%.