Can someone please explain how to calculate "percent more than" and "percent less than"?
I know $35$ is $75$ percent more than $20$ - but no idea how to calculate it.
Also trying to figure out how to find percent less than for: $120$ is what percent less than $200$?
Thank you!
On
$35$ is $75$ percent more than $20$
This implies $35-20=75$% of $20$
$120$ is what percent less than $200$
Here if the answer is $x$%, then we have the equation $200-120=x$% of $200$
Can someone please explain how to calculate "percent more than" and "percent less than"?
If $x$ is $m$ % more than $y$ then it implies $x-y=m$% of $y$
AND
If $p$ is $n$ % less than $q$ then it implies $q-p=n$% of $q$
You know that $35$ is $75\%$ more than $20$ because $$20 + (0.75)\cdot 20=20+15=35.$$ That is, if you compute $75\%$ of $20$ and add it to $20$, you get $35$. Let's see what $75\%$ less than $20$ is. Following the same logic as above, we should compute $75\%$ of $20$ and then subtract it from $20$: $$20-(0.75)\cdot 20 = 20-15 = 5.$$ That procedure is really all you need to know. $y$ is $r$ percent more than $x$ if $$y=x+\left(\frac{r}{100}\right)\cdot x$$ and $y$ is $r$ percent less than $x$ if $$y=x-\left(\frac{r}{100}\right) \cdot x.$$ Your second question asks: $120$ is what percent less than $200$? This is a "percent less than" problem, so we'll use the second equation that has the minus sign. We want to find the value of $r$ that makes the sentence "$120$ is $r$ percent less than $200$" true. So we see that $120$ is taking the place of $y$ and $200$ is taking the place of $x$. You're asked to find $r$, which you should now be able to do with some algebra.