Respuesta :
Answer:
[tex]1\frac{1}{4}\text{ or }1.25[/tex] cups of heavy cream.
Step-by-step explanation:
Let x represent cups of heavy cream and y represent cups of whole milk.
We have been given that a recipe calls for 2 cups of a mixture. We can represent this information in an equation as:
[tex]x+y=2...(1)[/tex]
We are also told that heavy cream is 36% butterfat, so butterfat in x cups of heavy cream would be [tex]0.36x[/tex].
We are also told that whole milk contains only 4% butterfat, so butterfat in y cups of whole milk would be [tex]0.04y[/tex].
The recipe calls for 2 cups of a mixture that is 24% butterfat. We can represent this information in an equation as:
[tex]0.36x+0.04y=2(0.24)...(2)[/tex]
From equation (1), we will get:
[tex]y=2-x[/tex]
Upon substituting this value in equation (2), we will get:
[tex]0.36x+0.04(2-x)=2(0.24)[/tex]
[tex]0.36x+0.08-0.04x=0.48[/tex]
Combine like terms:
[tex]0.32x+0.08=0.48[/tex]
[tex]0.32x+0.08-0.08=0.48-0.08[/tex]
[tex]0.32x=0.40[/tex]
[tex]\frac{0.32x}{0.32}=\frac{0.40}{0.32}[/tex]
[tex]x=\frac{40}{32}[/tex]
[tex]x=\frac{5}{4}[/tex]
[tex]x=1\frac{1}{4}[/tex]
[tex]x=1.25[/tex]
Therefore, [tex]1\frac{1}{4}\text{ or }1.25[/tex] cups of heavy cream should be used to produce the correct butterfat percentage.
