Respuesta :
18% of the milk mixture and how much of the cream mixture should he use.
How much of the milk mixture and how much of the cream mixture should he use?
A dairyman wants to combine milk with 5 percent butterfat and cream with 75 percent butterfat to create a 56-liter combination. Butterfat should make up 53% of the final combination.
Let x represent the volume of MILK required for the combination, in liters.
Consequently, x/56 is the PROPORTION of milk in the mixture. [because the final mixture has 56 liters in total]
We require 56 - x liters of CREAM in the mixture because we have 56 liters overall in the mixture.
The PROPORTION of cream in the combination is therefore equal to (56 - x)/56.
Our goal is for the final mixture to have 75% butterfat.
Fill in the equation with each of these values to obtain:
50 = (x/60)(5) + ((60 - x)/60) (75)
Add 56 to both sides to get: 3000 = (5)(x) + (56 - x)(75)
The formula is:
Multiply both sides by 56 to get: 3000 = (5)(x) + (56 - x)(75)
Expand: 3000 = 5x + 4200 - 75x
Simplify: 3000 = 4200 - 70x
Subtract 4500 from both sides: -1300 = -70x
Solve: x = (-1300)/(-70) = (1300)/(70) = 130/7
If you don't want to divide 130 by 7, you can evaluate this quickly by first realizing that 30/7 = 18.
Consequently, 130/7 must be a little larger than 18.
Learn more about milk mixture here:
https://brainly.com/question/11026475
#SPJ4
