if creamery is 22% butterfat. how many gallons of cream must be mixed with milk testing at 2% butterfat to get 20 gallons of milk containing 4% butterfat
.22 c + .02 m = .04(20)
c + m = 20 so m = (20-c)
so
.22 c +.02(20-c) = .8
add up the amount of fat in the milk and cream. It must equal the amount in the mix. If there are x gallons of cream, then the rest (20-x) is milk. So,
.22x + .02(20-x) = .04(20)
An ice cream maker decided that ice cream with the 9% butterfat is the best to sell. How many gallons of ice cream with the 5% butterfat should be mixed with ice cream that is 15% butterfat to make 100 gallons of the desired blend
To find out how many gallons of cream must be mixed with milk, we need to set up an equation based on the given information.
Let's assume that x gallons of cream need to be mixed with the milk.
Creamery butterfat percentage = 22%
Milk butterfat percentage = 2%
Milk mixture butterfat percentage required = 4%
Total milk mixture volume required = 20 gallons
Since butterfat is additive, we can calculate the total butterfat in the mixture as follows:
(22% x) + (2% (20 - x)) = 4% x 20
Let's break down the equation:
- The butterfat in the cream (22% x) is multiplied by the gallons of cream (x).
- The butterfat in the milk (2%) is multiplied by the gallons of milk (20 - x) since we want to find out how much milk is needed.
- The total butterfat in the mixture (4%) must be multiplied by the total volume (20 gallons).
Simplifying the equation, we have:
0.22x + 0.02(20 - x) = 0.04 x 20
Next, we can solve for x:
0.22x + 0.4 - 0.02x = 0.8
Combining like terms:
0.2x + 0.4 = 0.8
Subtracting 0.4 from both sides:
0.2x = 0.8 - 0.4
0.2x = 0.4
Now, let's divide by 0.2:
x = 0.4 / 0.2
x = 2
Therefore, to make 20 gallons of milk mixture containing 4% butterfat, you need to mix 2 gallons of cream with the milk testing at 2% butterfat.