I finally understand why Wall Street and political polling firms use "points" to describe a numerical change. But let's get to the problem.
Maker's Mark announced a couple days ago that they would begin diluting their product slightly more. What was the amount? Well, a bottle of regular Maker's Mark bourbon used to be 45% alcohol by volume. The liquor company will now sell it at 42%.
There were a lot of snobs out in full force, and I happened to catch a thread in a forum I frequent about the topic. And the math on display was not pretty. So I'm going to pose the same question to you:
Maker's Mark produces 6 million bottles of Bourbon whiskey per year and each bottle contains 45% alcohol by volume. Due to extraordinary demand, especially overseas, the decision was made to water down the product slightly to 42% alcohol by volume. How many additional bottles of whiskey will Maker's Mark now be able to produce?
If you got the right answer, congratulations, you're probably in pretty exclusive company. If you gave this question to Americans from ages 18-49, I doubt you'd more than 10% of them would get the answer correct. We don't teach our students math very well, and because it is so frustrating initially, many people will simply give up on the subject in middle school.
The correct answer is about approximately 428k bottles.
6 million * .45 = 6 million * .42 * x, solve for x.
.45/.42 = x = 1.0714
Multiply 6 million by 1.0714 and you get 6,428,400.
A lot of people would have looked at 45% and 42% and think: hmm, that's a difference of 3%. But it's actually much more than that. Because % means per cent. As in, per 100. It's really a difference of 3 per 45 (or 42, depending on how you choose to calculate the relative difference). And because people get tripped up on that simple mathematical concept, they won't be able to correctly answer that simple math problem.
This is a major problem with our education system. A poor foundation in math generally means you won't be good at financial problems. And if we, in aggregate, aren't good at those types of problems, we have a weaker national economy.
If you have kids, make sure they have an absolutely rock solid grasp on basic arithmetic and algebra by the time they enter high school. Because that's really all the math they'll ever need in the real world. And that knowledge gives you a lifelong benefit.