## Discoveries + Breakthroughs: Doing the Math to Become a Smarter Shopper

July 10 , 2007

Which one of the following two sales pitches is more likely to persuade a shopper to spend money: "Buy one, get one free" or "Buy two, get 50% off"? The two offers are really the same, but most consumers would find the first offer more appealing, so that's the one that most merchandisers use. TV viewers recently obtained a glimpse of the role that mathematics can play in helping people become smarter shoppers.

In this episode of the syndicated TV series Discoveries and Breakthroughs Inside Science (DBIS), physicist Joseph Ganem of Loyola College in Baltimore provided some examples of how simple math can help sort of all sorts of sales pitches, allowing consumers to tell true bargains from sneaky ploys. Ganem is author of the book The Two-Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy.

Many ads, like those for credit cards, are misleading. "A lot of the real facts are buried in the small print," Ganem says.

People tend to respond positively to large numbers. So, AOL offers 1,000 free Internet hours for 45 days. But there are 1,080 hours in the same number of days. "What the ad really means is a 45-day free trial period," Ganem says, "but they don't phrase it that way. They make you do some multiplication to find that out."

Food packaging can also create false impressions. Compare a soft drink that has 39 grams of sugar and 140 calories per serving to a fruit drink with 31 grams of sugar and 120 calories. But the serving size of the soft drink is 12 ounces, while the fruit drink is only 8 ounces. So ounce for ounce, the soft drink has fewer calories and less sugar than the fruit drink.

"If you have a calculator and can do some basic arithmetic, that's all you really need to make your own purchasing decisions," Ganem says.

"Become a Smarter Shopper" is just one of a wide range of mathematical, scientific, and technological topics covered in the DBIS series. The American Institute of Physics produces these science news programs, with the MAA as a contributing partner. The NSF-funded DBIS project delivers twelve 90-second segments each month for showing on local TV stations across the country.