Say trail mix (peanuts, cashews, raisins, and M&Ms) costs $1.50 a pound.

How do I do the math to tell whether it’s cheaper to buy peanuts, cashews, raisins, and M&Ms separately? I probably knew how to do this from the time the teacher taught it until about 5 minutes after the test, but that was during the Carter administration, and I’m completely at a loss now.

You need to know:
(1) the proportion of the various items in the trail mix, and
(2) the price of those items separately.

Suppose 1 pound of trail mix contains 4 oz of peanuts, 2 oz of cashews, 7 oz of raisins and 3 oz of M&Ms, then you need to work out how much that quantity of each costs, and add them up to see if it’s more or less than the $1.50.

If you want to mix them in equal proportions by weight, just add the per-pound prices for the individual ingredients, and compare to the same weight in trailmix. In other words, one pound of peanuts plus one pound of cashews plus one pound of raisins plus one pound of M&Ms should be cheaper than $6, which is the price of the four pounds of trailmix you can whip up yourself that way.

In other words, the average price-per-pound of the ingredients, which you calculate by adding up their individual prices and dividing by 4, should be less than the price-per-pound of the trailmix.

If the proportions are not equal, you need to add them proportionally as well. Let’s say that trailmix consists of 30% peanuts, 30% cashews, 25% raisins and 15% M%Ms. Then you calculate: 0.3 * the price of a pound of peanuts, plus 0.3 * the price of a pound of cashews, plus 0.25 * the price of a pound of raisins, plus 0.15 * the price of a pound of M&Ms. If that results in a value which is less than the price of a pound of trailmix, you should buy the separate ingredients and mix them up yourself.

Well, you also have to factor in your time to prepare them. If you consider your time to be $50/hour and it takes 15 minutes to pour out each ingredient, measure, shake and mix, repackage into individual ziploc bags, etc.

Also have to factor in the cost of the ziploc bags (if for example, you’re packaging individual servings for your school children.)

Basically, you may come to the conclusion that you should start a trail mix company in your kitchen and the profits will let you become fabulously wealthy.

I’m deeply torn between which of three things in this post amuse me more: that my time could be worth $50/hr, that I might have children, or that I could ever be fabulously wealthy.