Starting with a given set of percentages:

Whole milk has 3.5 percent butterfat.
Heavy cream has 36 percent butterfat.
Light cream has 20 percent butterfat.
Half-and-half has 10 percent butterfat.

How much heavy cream added to 1 cup 240 ml whole milk will equal a 10% butterfat mixture?
Light cream?
Half-and-Half?

59.15ml of heavy.

Or 153.16ml of light.

H/H will never get you there. You can't get to 10% concentration without having something stronger than 10% to get you there.

Just do weighted averages.

Thank you for the info.
I am not familiar with weighted averages.

My practical use of math ends with Pythagora's theorem and some uses for cross multiplying.

This started with a discussion of making a half-and half for a recipe if we only had milk and cream on hand.

TotFat/TotVol=.1
1cup*.035+Xcup*.36=TotFat
1cup+Xcup=TotVol

(1cup*.035+Xcup*.36)/(1cup+Xcup)=.1

.035cup+.36Xcup=.1cup+.1Xcup

.26Xcup=.065cup

X=.25 cups of Heavy Cream
(1/4cup)

——————————

TotFat/TotVol=.1
1cup*.035+Xcup*.20=TotFat
1cup+Xcup=TotVol

(1cup*.035+Xcup*.20)/(1cup+Xcup)=.1

.035cup+.20Xcup=.1cup+.1Xcup

.1Xcup=.065cup

X=.65 cups of Light Cream
(about 2/3cup)

——————————

Not possible with Half-Half.

——————————

Generic solution:

X1= % concentration
Y1= volume
X2= % concentration
Y2= volume
Xn= % concentration
Yn= volume

(X1*Y1+X2*Y2+…+Xn*Yn)
———————————— = Finished %
(Y1+Y2+…+Yn)

It is possible with half and half - use it unadulterated.

Throw the milk away and add 240 ml half and half.

This thread is still alive? lol