How many gallons of cream which is 10% butterfat must be added to 15 gallons of cream which is 20% butterfat to obtain cream which is 16% butterfat?
Oh, the delightful world of dairy math! Let me calculate that for you, but first, let's have a moment of silence for all the lactose intolerant souls out there.
To obtain a cream mixture that is 16% butterfat, we need to determine how much 10% butterfat cream to add to 15 gallons of 20% butterfat cream.
So let's get down to business. We'll use "x" to represent the gallons of cream to be added.
The amount of butterfat in the 10% cream can be calculated as 0.10x, and the amount in the 20% cream can be calculated as 0.20(15).
Now, when we mix these together, the total butterfat in the mixture will be 0.10x + 0.20(15). And this mixture should equal 16% of the total volume, which is 15 + x gallons.
Putting it all together:
0.10x + 0.20(15) = 0.16(15 + x)
Now we just need to solve the equation and find the value of "x."
0.10x + 3 = 2.4 + 0.16x
Rearranging a bit:
0.10x - 0.16x = 2.4 - 3
-0.06x = -0.6
Dividing both sides by -0.06:
x = 10
Hurray! The solution is in! You need to add 10 gallons of 10% butterfat cream to 15 gallons of 20% butterfat cream to obtain 16% butterfat cream... and keep in mind, folks, no dairy-themed clown acts were harmed in the making of this solution!
To find out how many gallons of cream with 10% butterfat need to be added to 15 gallons of cream with 20% butterfat to obtain cream with 16% butterfat, we can use a weighted average formula.
Let's assume x gallons of cream with 10% butterfat are needed.
The amount of butterfat in 15 gallons of cream with 20% butterfat is 15 * 20% = 3.
The amount of butterfat in x gallons of cream with 10% butterfat is x * 10% = 0.1x.
The amount of butterfat in the final mixture (15 + x gallons) with 16% butterfat is (15 + x) * 16% = 0.16(15 + x).
According to the weighted average formula, the sum of the butterfat in the initial mixtures is equal to the butterfat in the final mixture:
3 + 0.1x = 0.16(15 + x).
Now, let's solve this equation to find x:
3 + 0.1x = 2.4 + 0.16x.
Subtracting 0.1x from both sides, we get:
3 = 2.4 + 0.06x.
Subtracting 2.4 from both sides, we get:
0.6 = 0.06x.
Dividing both sides by 0.06, we get:
x = 0.6 / 0.06 = 10.
Therefore, 10 gallons of cream with 10% butterfat must be added to 15 gallons of cream with 20% butterfat to obtain cream with 16% butterfat.
To find out how many gallons of cream with 10% butterfat need to be added to 15 gallons of cream with 20% butterfat to obtain cream with 16% butterfat, you can use the method of solving mixtures.
Let's assume x gallons of cream with 10% butterfat are added to the existing 15 gallons of cream with 20% butterfat.
The total volume of the mixture will be given by:
15 + x
The percentage of butterfat in the mixture will be given by:
(15 * 20 + x * 10) / (15 + x) = 16
Now, we can solve this equation to find the value of x.
15 * 20 + 10x = 16 * (15 + x)
300 + 10x = 240 + 16x
6x = 60
x = 10
Therefore, 10 gallons of cream with 10% butterfat should be added to 15 gallons of cream with 20% butterfat to obtain cream with 16% butterfat.