what's the better deal? 0.32oz for \$23 or 0.21oz for \$14

Question

just want somebody to check if I'm doing this right

my process is to divide cost/weight

23/0.32 = 71.88

and

14/0.21 = 66.67

so the 2nd option is a better deal because I'm spending ~66 for 1 oz rather than ~71 for 1oz

is that correct?

Answer 1

It may be easier to compare the amount you get for a certain amount of money, so "one dollar buys three ounces". That way you choose the option where the number comes out larger.

In that case you want to divide the weight you get by the dollars, so weight divided by cost gives you amount per dollar. If you get 0.32 ounces for 23 cents, you get 1.39 ounces per dollar, and if you get 0.21 ounces for 14 cents, you get is 1.5 ounces per dollar, so the 0.21 ounces for 14 cents gives you more return for one dollar.

What you've calculated is what supermarkets usually display, the "unit cost", the cost for one pound, one ounce, one kilogram, one can, one package, etc. In that case you would choose whichever is the lowest price for one unit of the thing.

Answer 2

You asked a question that is not mathematical.

I assume that your prices are for buying a quantity of some substance S, which can be bought in two specific quantities at certain prices.

If you require a certain amount of S and want to pay the lowest possible price, you have an optimisation problem. The solution is obvious if you need up to 0.21, 0.32, 0.42, or 0.53 ounces. For larger quantities it is likely that some mix of the two quantities is optimal, say for 10 or 20 ounces. You solve this as an integer linear programming problem.

Alternatively, you might get some value from S, which probably doesn’t grow linear. For example, two burgers might be twice as nice for you as one if you like to eat a lot, but 10 are not. Now if you have a group of 6 people, 10 burgers might actually be quite bad because you get arguments who will only get one. 12 burgers may have much more than 20% higher value.

Again you have an optimisation problem that may require considerable effort creating a mathematical model before you can find an optimal answer.

After reading the comments, a third case. Assume you run a restaurant that offers free sachets of mustard (mustard might come in these tiny portions). If the portions are large, people take one sachet. If you use smaller sachets, some percentage of customers take two. To find the best product to pay, it’s best to experiment and find how many sachets and therefore how much of your money customers take depending on the size, and then you choose the optimal size.