## Sunday, October 26, 2008

### Different Ways to Do Percentage Differences

Kitty weighs eight pounds. Fido is 300% heavier than Kitty. How much does Fido weigh?

24 pounds is the intuitive answer for many people, but 32 pounds is correct.

To clarify, let’s try this: Kitty weighs eight pounds. Fido is 24 pounds heavier than Kitty. How much does Fido weigh?

32 pounds, of course.

In the second example, it’s clearer that “24 pounds heavier” refers to the difference between Fido’s and Kitty’s weights. Now apply that same concept to the original example, so that the difference between Kitty’s and Fido’s weights is 300% of Kitty’s weight. That difference is 8 pounds multiplied by 300%, which is 24. Thus, Fido is 24 pounds heavier than Kitty, which makes Fido’s weight 32 pounds.

Got it? Well, there’s one more twist, which is the part worth remembering.

I could have made the original question easier by saying Fido’s weight is 400% of Kitty’s weight. This means the percentage applies directly to Kitty’s weight, so we’d just multiply 8 pounds by 400%, which is 32 pounds.

This latter method is simpler to calculate and to explain. So if you need to compare numbers using a percentage, and especially if the percentage is going to be above 100, avoid terms like “heavier,” “greater,” and the like, and don’t calculate on the difference.

Just remember X is n% of Y (like “Fido’s weight is 400% of Kitty’s weight”). It is easier to understand and calculate.