My daughter asked me for a formula/equation.
I can't provide it.
Half and half is 3.5 g. fat per 30 ml. serving.
2% milk is 5 g. fat per 240 ml. serving.
How much of each product need to be combined to equal a 240 ml. serving of 3.5% fat (whole milk equivalent)?

The fat content percentage of Half and Half is necessary to answer your question.

It's stated in the OP.
The ratio is in the OP for half and half.
"2%" for the milk is nominal I believe. 240 times 2% = 4.8 g. fat which is rounded up to 5 g. on the label.

Half & Half is 10%

30 plus years working in Dairy

It's worse than she thinks.  She needs two equations.

x + y = 240 ml

x(3.5g/30ml) + y(5g/240ml) = 8.4g

My gramma had a milk pitcher when I was a kid. My guess is it was probably made in the 1920s or 1930s.
It had various things written on it. It said "Whole milk contains 10% cream". I wonder when the USDA standard changed (or if it even was the USDA that specified whole milk fat content).

I will show her this.
This started as a mental exercise for the fun of it.
Thanks.

Can you show your work for the answer?

My daughter thinks she has the answer. She used the elimination method found in an algebra book in a chapter titled Systems of Linear Equations and Problem Solving.
She came up with x=.25 and y=.7 for a ratio.
I would still like to see someone correctly write out the problem showing their work.
TIA.

First, You need to figure out how much fat is in the 240 ml of whole milk.  If 2% milk has 5g, then 3.5% milk should have (3.5/2 * 5g) 8.75g of fat.

Next, let's get all of our fat contents to be in the same "units."  In this case, we'll find the total amount of fat in 240 ml, since 2 of them are already there and the other is easy to find out.

So, since Half and Half is 3.5 g of fat per 30 ml, there will be 8 times that (240/30) in 240 ml, or 28 g of fat.

Now, we can consider the amounts of fat to be our baseline.  We want 8.75 g of fat, and to do it we add a portion of each, the total portion of which becomes 1 (the baseline).

So, we have X of half and half, and (1 - X) of 2% milk, and the total fat is (X * 28) + ((1 - X) * 5), and the total is 8.75.  So your formula is (28 * X) + 5 - (5 * X) = 8.75

Simplify and solve for X.  X will be the portion of your 240 ml that is Half and Half, and (1 - X) will be the portion that is 2% milk.  Simply multiply by 240 ml to get the volume of each.

Mike

ETA:  Simplifying, we get 23 * X = 3.75, and X = 0.163.  So we are proportions are 0.163 of Half and Half, and .837 of 2% milk.  We multiply by 240 ml to get 39.13 ml of Half and Half, and 200.87 ml of 2% milk.  The total fat is (0.163 * 28) + (0.837 * 5) = 8.749g, which is within our rounding error.

Thank you for the explanation!

The definition of 'cream' fat content is not a single value.

The cream a restaurant typically purchase and uses has a higher fat content than the typical level you purchase at the grocery store.

It is one of the 'tricks' that makes the restaurant food taste better.

Bakers also have easy access to higher fat cream.

They can tell the supplier what fat level they want across a range of available levels.


But it is all 'heavy cream.'