Dr. Dave Science

In my last post I talked about the importance of doing math in your head and using estimates to make it easier. My example focused on flying because it is something that I enjoy doing and math plays a key role in it.

I was thinking that I needed a better example, an everyday example. I found it when I went shopping for shoes last week.

With winter on its way out, several stores are having their annual “end of winter sale.” I live in Chicago and I like to be outdoors. This means that I need a good pair of boots that can withstand the cold, keep the slush out, and be comfortable to walk in.

In one shoe store, I found a pair of high quality boots that originally cost $84.99, and were on sale for 35% off. Using a few simple math tricks, I was able to calculate how much the shoes would cost in my head.

Why bother doing the math? You will find that out in the end.

How did I do the math? Let me share this with you now.

Simplify the problem!

$84.99, is a hard number to use. When I was younger, I thought that the $0.99 at the end of every price was put there to scare me away from doing math in my head. This is a lame excuse. I quickly learned to round the prices up to make the number easier to handle. In this case we will use $85.

Percentages are also a intimidating, especially for a number like 35%. The key to figuring out percentages is to break it down into simpler numbers. When calculating a sale price I find that the easiest percentages to calculate are 50%, 10%, and 5%.

I selected these numbers because…

50% is half, so divide the price by two.

10% is 1/10, so divide the price by 10.

5% is half of 10%, so determine the 10% price and then divide it in half.

For numbers like 35%, use a combination of the numbers above. For example, the number 35 breaks down into 10 + 10 + 10 + 5, or (3 x 10) + 5.

Since the boots cost $85, 10% is $8.50 and 5% is half of the 10% price, or $4.25. To figure out what 35% is, multiply (3 x $8.50) and then add $4.25.

Ok, I know you are thinking that 3 x $8.50 is not simple math.

Here’s how I see it. I know that 3 x $8 is $24 and 3 x $0.50 is $1.50. Add them together to get $25.50. Doing math this way makes the problem easier to solve.

To figure out the final discount, add $4.25 and $25.50. This gives $29.75 for the 35% price. That’s nearly $30 off!

This means I should pay about $55 before taxes. The actual price is $55.24, so our estimate is very good.

So why bother doing the math?

When I asked people about how they solve this kind of math problem, most said that they trust the register so they do not worry about doing math in their head.

I disagree with them because I have had many experiences like the one below.

When I took the boots to the register, I was expecting the price to be around $55. The clerk scanned the shoes and the computer said the shoes cost $63.74.

There had to be a mistake somewhere.

I quickly estimated that $63.74 reflected 25% off, not the 35% that was advertised. How did I do this?

I figured this out by first rounding $63.74 up to $64 because it is easier to deal with.

The difference between $64 and $55 is $9. This is close to $8.50, or about 10% (we figured this out earlier). Since the price rang up higher, that means the discount was 10% less than 35%, giving 25%.

I told the sales clerk that that the shoes were on sale for 35%, not 25%. As it turns out, the same pair of shoes were on sale last week for 25%, and this week they were on sale for 35%.

The register was not updated with the new price.

By doing math in my head I was able to catch the mistake. If I had trusted the register, I would have paid $9 more than I should have.

With $9 I could buy lunch or about 3 gallons of gas.

What could you do with $9?

-Dr. Dave