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Math Tips for Smart Shopping

Would you rather get a 33% bigger coffee for no extra charge or pay 33% less for the regular size? Do you know how to avoid being tricked into buying more than you need? Keep on reading The Math Dude to learn about the number behind savvy shopping.

By
Jason Marshall, PhD
Episode #226

I recently ran across a 2012 article from The Atlantic called The 11 Ways That Consumers Are Hopeless at Math. The title of this article hooked me, and as I began reading I found that there are indeed a few ways in which consumers misunderstand math - and pay the price as a result.

But I also found that most of the so-called “math tricks" that people get caught up in are really better described as number-based psychological hacks, which marketers use to extract every last penny from us that they can.

So it's not so much that consumers are hopeless at math as they are susceptible to being tricked. Which is precisely what a savvy shopper knows how to avoid.

What are some of these mathematical misunderstandings that you should be aware of? And what are some of the most common number-based psychological hacks? Those are exactly the questions we’ll be looking at today, as we finish up the year with a resolution to become even smarter shoppers in the new year..

How Much Bang For Your Buck?

The article I mentioned from The Atlantic begins with an anecdote that nicely points out one of the biggest flaws in the way the average consumer shops. Namely, that when it comes to pricing and deals, most people go with their gut instead of taking a few seconds to think things through.

Here's the story: Imagine you walk into a coffee shop, take a look at the day’s specials, and see a sign that says, “Today only, your choice—get 33% more coffee for the regular price, or pay 33% less for the regular amount of coffee!” If you were presented with these two options, which would you choose?

In truth, choosing the best deal isn't always just a question of numbers. For example, if you really wanted more than your regular amount of coffee that day, then the extra coffee option would be a fine choice. But that’s not really what I’m talking about here, so let’s rephrase the question a bit to focus on the math.

The real question is this: Which option is the better deal in terms of dollars spent per ounce of coffee? After all, that’s what we’re really talking about when we speak of being a savvy shopper—getting the most bang for your buck.

Most people's gut instinct is that the two deals are about equally as good.

Most people’s gut instinct is that the two deals—33% more coffee for the same price or the same amount of coffee for 33% less money—are equally as good. After all, they both have the same 33% in them. But let’s do the math to see if this assumption is really true.

Imagine your usual 8 oz. cup of coffee costs \$2. In this case, the first option gives you about 1.33 x 8 oz. = 10.6 oz. of coffee for \$2, while the second option gives you your usual 8 oz. of coffee for a price of 0.67 x \$2 = \$1.34. That means you pay \$2 / 10.6 oz. = 18.9 cents/oz. with the first option, but only \$1.34 / 8 oz. = 16.8 cents/oz. with the second.

So, clearly, the second option is a better deal. While it's tempting to get something "free" for the same amount you usually pay (the first option), in this case, getting the amount you actually want for less money is a better deal—especially if you don't really need that extra coffee anyway. And, as always, the math is there to back you up.