% Increase/Decrease Formula vs Ratios

[wsypinero]

Often times I use the formula (end-begin)/begin to get the increase/decrease.

However, I used the same approach to a question that asked "how many times more paint does the larger circle need than the smaller circle." This was a ratio question of 4x:1x and the right answer was 4. However, if i used the (end-begin)/begin, I would get 3.

Is there a way to avoid this confusion? Are there key words that I can use to confirm which approach is correct.

please advise - Thanks!

[Ben Ku]

Reading and understanding the wording is very important in these kinds of questions. Do not simply rely on a formula.

Suppose the area of the P is 4x and area of the S is x.

There are different questions that can be asked:
(1) How much larger is the area of Circle P than Circle S?
Here, the question asks for the DIFFERENCE between the areas because it's asking how MUCH (that's the key word). The Circle P is 3x larger than Circle S.

(2) How many times larger is the area of Circle P than Circle S?
Here, the question asks for the RATIO of the areas, because it's asking how many TIMES (that's the key word). The ratio is 4x:x = 4. Circle P is 4 times larger than Circle S.

The formula you use is specifically for percent increase or decrease. Hope that helps.