A is x% more than B

Question

I am taking the AMC10 test, and I don’t want to lose points on silly misunderstandings. When a question says “A is x% greater/less than B”, or things like that sometimes with money, which respect should we take if it doesn’t tell me which? And please write a formula to make it clear. Thanks!

Answer 1

Whenever you are given that a quantity $A$ is $x\%$ greater or less than $B$ the first thing is that the comparision is done with respect to the quantity $B$.

Look it in another way. So how do you calculate the $\%$ increase or decrease in a quantity with respect to another quantity.

If it is said that the quantity $A$ is $x\%$ greater than quantity $B$ what you mean is : $$\frac{A-B}{B}=\frac{x}{100}$$ And if the quantity is $x\%$ less than $B$ then : $$\frac{B-A}{B}=\frac{x}{100}$$ Hope this helps ...

Answer 2

Not exactly sure what you're asking, but, I guess, a statement like "$A$ is $x\%$ greater than B" formulaically should be interpreted as follows:

$$ A=B+\frac{B}{100}\cdot x=B\left(1 + \frac{x}{100}\right) $$

Likewise, "$A$ is $x\%$ less than B" should be understood like this:

$$ A=B-\frac{B}{100}\cdot x=B\left(1 - \frac{x}{100}\right) $$

So, I guess you could say you're calculating percents with respect to $B$.