Sunday, February 17, 2008

Dinner and a Math Challenge

Well, the February meals are under way. Last night Daniel served BLT hot dogs, baked beans, winter fruit salad, and tossed salad, followed by homemade vanilla ice cream with bittersweet chocolate shavings. I did persuade him to buy the hot dog buns--the cook book had a recipe for homemade.

The hot dogs were simple but good. Hot dogs (we splurged on Nathan's) were each wrapped in a slice of bacon and then baked at 375* for 45 minutes. I didn't believe they would take so long, but they really did need the full time. They were served with diced tomato, shredded lettuce, and mayo (as well as the usual condiments), but I think they were better without.

We make ice cream by cooking the custardy base a day ahead so the eggs are safe (former dietitian bacteria phobe!) and everything has time to chill. On Friday this gave me a chance to give Daniel a different sort of math assignment--recipe manipulation. It went something like this:

The recipe calls for 1 2/3 cups of milk. The texture of ice cream is strongly affected by appropriate fat content, so we need to use the whole milk the recipe is assuming. However, we don't keep whole milk in the house. So figure out how much low fat milk and half-and-half we need to use to "make" whole milk. Make the calculations, but also explain how you would measure it in real life.

Given:
1 cup low fat milk= 2.5 g fat
1 cup whole milk= 8 g fat
1 cup half-and-half= 24 g fat

If you're interested in giving this a try, the answer is in the comments, along with the follow up question that I gave to Daniel.

By the way, the ice cream was delicious! We usually us The Ultimate Ice Cream Book, given to us by those wonderful Nelsons.

1 comment:

Barbara said...

Ice Cream Math Solution
H=amount of half-and-half
L=amount of low fat milk
W=amount of whole milk=1 2/3 cup=5/3 cup

Since we know W, there are really only two variables, so we need two equations. Here is the one for the amount of milk products needed:

H + L = 1 2/3 = 5/3

Here is the one for the amount of fat needed:

24H + 2.5L = 8W, which becomes
24H + 5/2 L = 8(5/3) = 40/3

There is more than one way to calculate from here, but here's ours:
Multiply the 1st equation by (-5/2) and then add it to the first equation. Now you have:
24H-(5/2)H = 40/3 - 25/6 = 80/6 - 25/6 = 55/6 = (48/2)H - (5/2)H = (43/2)H

With a little more math, you end up with H = 55/129, which you just have to solve with long division, to give H = .42 (cups of h&h). That's not an easy amount in real life, so go back to W, which is 1 2/3, or 1.67 cups whole milk. 1.67 - .42 + 1.25 cups of low fat milk. Now it's easy: measure 1 1/4 cups low fat milk, then add half and half until it hits the 1 2/3 cup mark. Voila! Whole milk!

As I went through the calculations before giving this to Dan, I wondered why it was so much trickier than the other times I've mixed milks. Then I remembered that I usually use skim plus whatever cream is around. So question #2 was to calculate the answer using skim rather than low fat milk.

As soon as he saw it, he groaned because it is so much easier! The earlier equation of 24H + 2.5L=8W became 24H + (0)S =8W, so S (skim) drops right out!

If you're really interested, this quickly resulted in H = 5/9, S= 10/9, which are close to 1/2 and 1, so it is easy to measure either product and then top off to 1 2/3.

Tired yet? This is what passes for fun when we're in a math mood.